Любашенко Володимир Васильович
Публікації
Монографiї
[I] Squared Hopf algebras, Mem. Amer. Math. Soc. 142 (1999), no. 677, 184 p.
[II] Non-semisimple topological quantum field theories for 3-manifolds with
corners, Lect. Notes in Math., vol. 1765, Springer-Verlag, Heidelberg,
2001, vi+379 p. (with T. Kerler).
[III] Pretriangulated A∞-categories, Proceedings of the Institute of
Mathematics of NAS of Ukraine, vol. 76, Institute of Mathematics of NAS
of Ukraine, Kyiv, 2008, 599 p. (with Yu. Bespalov and O. Manzyuk).
Статтi
[1] Граничнi значення розв’язкiв диференцiально-операторних рiвнянь, Доповiдi
АН УРСР, Сер. A. (1984) n. 4, 71–73 (з О. Г. Резнiковим).
[A] Интеграл на обобщенных многообразиях, Тезисы докладов XI Всесоюзной шко-
лы по теории операторов в функциональных пространствах, Челябинск, май
1986, с. 80.
[B] Уравнение треугольников и оператор четности, Тезисы докладов XI конфе-
ренции математиков высших учебных заведений Грузинской ССР, Кутаиси,
май 1986, с. 151.
[2] Березиниан в некоторых моноидальных категориях, Украинский Матем.
Журнал 38 (1986) n. 5, 588–592.
[3] Алгебры Хопфа и вектор-симметрии, Успехи Матем. Наук 41 (1986) n. 5, 153–
154.
[4] Суперанализ и решения уравнения треугольников, Диссертация кандидата
физико-математических наук, Киев, 1986.
[5] Real and imaginary forms of quantum groups, Quantum Groups, Lect. Notes
Math., vol. 1510, Springer, 1992, 67–78.
[6] Categorical aspects of conformal field theory, CMS Conference Proceedings
(R. A. G. Seely, ed.), vol. 13, 1992, 309–320.
[7] Fourier transform identities in quantum mechanics and the quantum line,
Phys. Lett. B 284 (1992), 66–70 (with S. Majid).
[8] Braided groups and quantum Fourier transform, J. Algebra 166 (1994),
no. 3, 506–528 (with S. Majid).
[9] Existence of R-matrix for quantized Kac–Moody algebra, Math. Proc. Camb.
Phil. Soc. 116 (1994), no. 2, 193–207.
[10] Quantum function algebra at roots of 1, Adv. Math. 108 (1995), no. 2,
205–262 (with C. De Concini).
[11] Tangles and Hopf algebras in braided categories, J. Pure and Applied
Algebra 98 (1995), no. 3, 245–278.
[12] Modular transformations for tensor categories, J. Pure and Applied Algebra
98 (1995), no. 3, 279–327.
[13] Modular properties of ribbon abelian categories, Symposia Gaussiana, Proc.
of the 2nd Gauss Symposium, Munich, 1993, Conf. A (Berlin, New York),
Walter de Gruyter, 1995, 529–579.
[14] Invariants of 3-manifolds and projective representations of mapping class
groups via quantum groups at roots of unity, Commun. Math. Phys. 172
(1995), no. 3, 467–516.
[15] Ribbon abelian categories as modular categories, J. Knot Theory
Ramifications 5 (1996), no. 3, 311–403.
[16] Extensions and contractions of the Lie algebra of q-pseudodifferential
symbols on the circle, J. Funct. Anal. 143 (1997), no. 1, 55–97
(with B. Khesin and C. Roger).
[17] Squared Hopf algebras and reconstruction theorems, Proc. of the Workshop
“Quantum Groups and Quantum Spaces” (Warszawa), Banach Center Publ.,
no. 40, Inst. Math. Polish Acad. Sci., 1997, 111–137.
[18] Quantum supergroups of GL(n|m) type: Differential forms, Koszul complexes
and Berezinians, Duke Math. J. 90 (1997), no. 1, 1–62 (with A. Sudbery).
[19] Generalised Lie algebras of type An , J. Mathematical Phys. 39 (1998),
no. 6, 3487–3504 (with A. Sudbery).
[20] Приклад триангульованої категорiї Хопфа, Вiсник Київського унiверситету,
серiя: фiз.-мат. науки, (1999) n. 2, 50–58.
[21] Operations and isomorphisms in a triangulated Hopf category, Methods of
Func. Analysis and Topology 5 (1999), no. 4, 37–53.
[22] Integrals for braided Hopf algebras, J. Pure and Appl. Algebra 148 (2000),
no. 2, 113–164 (with Yu. Bespalov, T. Kerler and V. G. Turaev).
[23] Тензорний добуток еквiварiантних збочених в’язок, Вiсник Київського унiвер-
ситету, серiя: фiз.-мат. науки, (2000) n. 2, 22–34.
[24] Coherence isomorphisms for triangulated Hopf category SL(2), Науковi
записки Нац. унiверситету “Києво-Могилянська академiя”, Фiзико-математичнi
науки, 18 (2000), 4–7.
[25] On a functorial isomorphism in the derived category of l-adic sheaves,
Matematychni Studii 14 (2000), no. 2, 115–120.
[26] Квадратовнi алгебри Хопфа та модулярний функтор, Дисертацiя доктора
фiзико-математичних наук, Київ, 2000.
[27] Зовнiшнiй тензорний добуток збочених в’язок, Укр. матем. журн. 53 (2001),
no. 3, 311–322.
[28] Coherence isomorphisms for a Hopf category, Noncommutative Structures in
Mathematics and Physics (Dordrecht) (S. Duplij and J. Wess, eds.), NATO
Advanced Research Workshop Proceedings, Kluwer Academic Publishers, 2001,
September 24-27, 2000, Kyiv, Ukraine, 283–294.
[29] Coassociativity–coherence relation for Hopf category n+ SL2, Третя мiжнар.
алгебр. конфер. в Українi, Суми, 2-8 липня 2001, 67–70.
[30] Tensor products of categories of equivariant perverse sheaves, Cahiers
Topologie Geom. Differentielle Categ. XLIII-1 (2002), 49–79.
[31] The triangulated Hopf category n+ SL(2), Applied Categorical Structures 10
(2002), no. 4, 331–381.
[32] A model of the 2-category of equivariant derived categories, Algebraic
structures and their applications (Kyiv), Inst. of mathematics NASU, 2002,
Proc. of Ukrainian Math. Congress – 2001, 307–322.
[33] Category of A∞-categories, Homology, Homotopy and Applications 5 (2003),
no. 1, 1–48, http://intlpress.com/HHA/v5/n1/a1/
[34] Category of A∞-categories and derived categories, Науковi записки Нац.
унiверситету “Києво-Могилянська академiя”, Фiзико-математичнi науки, 21
(2003), 5–20 (with S. A. Ovsienko).
[35] Спецiальнi опори i гомотопiчнi бiалгебри, Математичний вiсник наукового то-
вариства iм. Т. Шевченка 1 (2004), 59–76.
[36] Free A∞-categories, Theory and Applications of Categories 16 (2006),
no. 9, 174–205 (with O. Manzyuk).
[37] Braided and modular tensor categories, Encyclopedia of Mathematical
Physics (J.-P. Francoise, G. L. Naber, and S. T. Tsou, eds.), vol. 1,
Elsevier Science Publ., Oxford, 2006, 351–359.
[38] A construction of quotient A∞-categories, Homology, Homotopy and
Applications 8 (2006), no. 2, 157–203 (with S. A. Ovsienko).
[39] Unital A∞ -categories, Проблеми топологiї та сумiжнi питання
(ред. В. В. Шарко), Зб. праць Iн-ту математики НАН України, том 3, no. 3,
Iн-т математики НАН України, Київ, 2006, стор. 235–268 (with O. Manzyuk).
[40] Erratum to: “Category of A∞-categories” [Homology, Homotopy Appl. 5 (2003),
no. 1, 1–48], Homology, Homotopy Appl. 9 (2007), no. 2, 163–164.
[41] A∞-bimodules and Serre A∞-functors, Geometry and Dynamics of Groups and
Spaces (M. M. Kapranov, S. Kolyada, Yu. I. Manin, P. Moree, and L. ,
Potyagailo eds.), Progress in Mathematics, vol. 265, Birkhauser Verlag,
Basel, 2008, 565–645 (with O. Manzyuk).
[42] Quotients of unital A∞-categories, Theory Appl. Categ. 20 (2008), no. 13,
405–496 (with O. Manzyuk).
[43] A∞-algebras, A∞-categories and A∞-functors, Handbook of Algebra, vol. 5,
Elsevier Science Publ., North Holland, 2008, pp. 143–188 (with O. Manzyuk).
[44] Homotopy unital A∞-algebras, J. Algebra 329 (2011), no. 1, 190–212,
Special Issue Celebrating the 60th Birthday of Corrado De Concini,
http://dx.doi.org/10.1016/j.jalgebra.2010.02.009
[45] Bar and cobar constructions for curved algebras and coalgebras,
Matematychni Studii 40 (2013), no. 2, 115–131.
[46] A∞-morphisms with several entries, Theory Appl. Categ. 30 (2015), no. 45,
1501–1551, http://www.tac.mta.ca/tac/volumes/30/45/30-45abs.html
[47] Homotopy unital A∞-morphisms with several entries, Theory Appl. Categ.
30 (2015), no. 46, 1552–1623,
http://www.tac.mta.ca/tac/volumes/30/46/30-46abs.html
[48] Homotopy cooperads, Математичнi Студiї 44 (2015), no. 2, 119–160,
http://matstud.org.ua/texts/2015/44_2/119-160.html
[49] Curved homotopy coalgebras, Appl. Categ. Structures 25 (2017), no. 6,
991–1036, https://doi.org/10.1007/s10485-016-9440-4
[50] Moyal and Rankin–Cohen deformations of algebras, Proc. Int. Geom. Cent. 11
(2018), no. 2, 48–52, https://doi.org/10.15673/tmgc.v11i2.1027
[51] Модельна структура на категоріях пов’язаних з категоріями комплексів,
Український математичний журнал 72 (2020), no. 2, 232–244,
http://umj.imath.kiev.ua/index.php/umj/article/view/682
Переклад в https://doi.org/10.1007/s11253-020-01780-3.
[52] Filtered cocategories, Theory Appl. Categ. 35 (2020), no. 47, 1726–1770,
http://www.tac.mta.ca/tac/volumes/35/47/35-47.pdf
[I] Squared Hopf algebras, Mem. Amer. Math. Soc. 142 (1999), no. 677, 184 p.
[II] Non-semisimple topological quantum field theories for 3-manifolds with
corners, Lect. Notes in Math., vol. 1765, Springer-Verlag, Heidelberg,
2001, vi+379 p. (with T. Kerler).
[III] Pretriangulated A∞-categories, Proceedings of the Institute of
Mathematics of NAS of Ukraine, vol. 76, Institute of Mathematics of NAS
of Ukraine, Kyiv, 2008, 599 p. (with Yu. Bespalov and O. Manzyuk).
Статтi
[1] Граничнi значення розв’язкiв диференцiально-операторних рiвнянь, Доповiдi
АН УРСР, Сер. A. (1984) n. 4, 71–73 (з О. Г. Резнiковим).
[A] Интеграл на обобщенных многообразиях, Тезисы докладов XI Всесоюзной шко-
лы по теории операторов в функциональных пространствах, Челябинск, май
1986, с. 80.
[B] Уравнение треугольников и оператор четности, Тезисы докладов XI конфе-
ренции математиков высших учебных заведений Грузинской ССР, Кутаиси,
май 1986, с. 151.
[2] Березиниан в некоторых моноидальных категориях, Украинский Матем.
Журнал 38 (1986) n. 5, 588–592.
[3] Алгебры Хопфа и вектор-симметрии, Успехи Матем. Наук 41 (1986) n. 5, 153–
154.
[4] Суперанализ и решения уравнения треугольников, Диссертация кандидата
физико-математических наук, Киев, 1986.
[5] Real and imaginary forms of quantum groups, Quantum Groups, Lect. Notes
Math., vol. 1510, Springer, 1992, 67–78.
[6] Categorical aspects of conformal field theory, CMS Conference Proceedings
(R. A. G. Seely, ed.), vol. 13, 1992, 309–320.
[7] Fourier transform identities in quantum mechanics and the quantum line,
Phys. Lett. B 284 (1992), 66–70 (with S. Majid).
[8] Braided groups and quantum Fourier transform, J. Algebra 166 (1994),
no. 3, 506–528 (with S. Majid).
[9] Existence of R-matrix for quantized Kac–Moody algebra, Math. Proc. Camb.
Phil. Soc. 116 (1994), no. 2, 193–207.
[10] Quantum function algebra at roots of 1, Adv. Math. 108 (1995), no. 2,
205–262 (with C. De Concini).
[11] Tangles and Hopf algebras in braided categories, J. Pure and Applied
Algebra 98 (1995), no. 3, 245–278.
[12] Modular transformations for tensor categories, J. Pure and Applied Algebra
98 (1995), no. 3, 279–327.
[13] Modular properties of ribbon abelian categories, Symposia Gaussiana, Proc.
of the 2nd Gauss Symposium, Munich, 1993, Conf. A (Berlin, New York),
Walter de Gruyter, 1995, 529–579.
[14] Invariants of 3-manifolds and projective representations of mapping class
groups via quantum groups at roots of unity, Commun. Math. Phys. 172
(1995), no. 3, 467–516.
[15] Ribbon abelian categories as modular categories, J. Knot Theory
Ramifications 5 (1996), no. 3, 311–403.
[16] Extensions and contractions of the Lie algebra of q-pseudodifferential
symbols on the circle, J. Funct. Anal. 143 (1997), no. 1, 55–97
(with B. Khesin and C. Roger).
[17] Squared Hopf algebras and reconstruction theorems, Proc. of the Workshop
“Quantum Groups and Quantum Spaces” (Warszawa), Banach Center Publ.,
no. 40, Inst. Math. Polish Acad. Sci., 1997, 111–137.
[18] Quantum supergroups of GL(n|m) type: Differential forms, Koszul complexes
and Berezinians, Duke Math. J. 90 (1997), no. 1, 1–62 (with A. Sudbery).
[19] Generalised Lie algebras of type An , J. Mathematical Phys. 39 (1998),
no. 6, 3487–3504 (with A. Sudbery).
[20] Приклад триангульованої категорiї Хопфа, Вiсник Київського унiверситету,
серiя: фiз.-мат. науки, (1999) n. 2, 50–58.
[21] Operations and isomorphisms in a triangulated Hopf category, Methods of
Func. Analysis and Topology 5 (1999), no. 4, 37–53.
[22] Integrals for braided Hopf algebras, J. Pure and Appl. Algebra 148 (2000),
no. 2, 113–164 (with Yu. Bespalov, T. Kerler and V. G. Turaev).
[23] Тензорний добуток еквiварiантних збочених в’язок, Вiсник Київського унiвер-
ситету, серiя: фiз.-мат. науки, (2000) n. 2, 22–34.
[24] Coherence isomorphisms for triangulated Hopf category SL(2), Науковi
записки Нац. унiверситету “Києво-Могилянська академiя”, Фiзико-математичнi
науки, 18 (2000), 4–7.
[25] On a functorial isomorphism in the derived category of l-adic sheaves,
Matematychni Studii 14 (2000), no. 2, 115–120.
[26] Квадратовнi алгебри Хопфа та модулярний функтор, Дисертацiя доктора
фiзико-математичних наук, Київ, 2000.
[27] Зовнiшнiй тензорний добуток збочених в’язок, Укр. матем. журн. 53 (2001),
no. 3, 311–322.
[28] Coherence isomorphisms for a Hopf category, Noncommutative Structures in
Mathematics and Physics (Dordrecht) (S. Duplij and J. Wess, eds.), NATO
Advanced Research Workshop Proceedings, Kluwer Academic Publishers, 2001,
September 24-27, 2000, Kyiv, Ukraine, 283–294.
[29] Coassociativity–coherence relation for Hopf category n+ SL2, Третя мiжнар.
алгебр. конфер. в Українi, Суми, 2-8 липня 2001, 67–70.
[30] Tensor products of categories of equivariant perverse sheaves, Cahiers
Topologie Geom. Differentielle Categ. XLIII-1 (2002), 49–79.
[31] The triangulated Hopf category n+ SL(2), Applied Categorical Structures 10
(2002), no. 4, 331–381.
[32] A model of the 2-category of equivariant derived categories, Algebraic
structures and their applications (Kyiv), Inst. of mathematics NASU, 2002,
Proc. of Ukrainian Math. Congress – 2001, 307–322.
[33] Category of A∞-categories, Homology, Homotopy and Applications 5 (2003),
no. 1, 1–48, http://intlpress.com/HHA/v5/n1/a1/
[34] Category of A∞-categories and derived categories, Науковi записки Нац.
унiверситету “Києво-Могилянська академiя”, Фiзико-математичнi науки, 21
(2003), 5–20 (with S. A. Ovsienko).
[35] Спецiальнi опори i гомотопiчнi бiалгебри, Математичний вiсник наукового то-
вариства iм. Т. Шевченка 1 (2004), 59–76.
[36] Free A∞-categories, Theory and Applications of Categories 16 (2006),
no. 9, 174–205 (with O. Manzyuk).
[37] Braided and modular tensor categories, Encyclopedia of Mathematical
Physics (J.-P. Francoise, G. L. Naber, and S. T. Tsou, eds.), vol. 1,
Elsevier Science Publ., Oxford, 2006, 351–359.
[38] A construction of quotient A∞-categories, Homology, Homotopy and
Applications 8 (2006), no. 2, 157–203 (with S. A. Ovsienko).
[39] Unital A∞ -categories, Проблеми топологiї та сумiжнi питання
(ред. В. В. Шарко), Зб. праць Iн-ту математики НАН України, том 3, no. 3,
Iн-т математики НАН України, Київ, 2006, стор. 235–268 (with O. Manzyuk).
[40] Erratum to: “Category of A∞-categories” [Homology, Homotopy Appl. 5 (2003),
no. 1, 1–48], Homology, Homotopy Appl. 9 (2007), no. 2, 163–164.
[41] A∞-bimodules and Serre A∞-functors, Geometry and Dynamics of Groups and
Spaces (M. M. Kapranov, S. Kolyada, Yu. I. Manin, P. Moree, and L. ,
Potyagailo eds.), Progress in Mathematics, vol. 265, Birkhauser Verlag,
Basel, 2008, 565–645 (with O. Manzyuk).
[42] Quotients of unital A∞-categories, Theory Appl. Categ. 20 (2008), no. 13,
405–496 (with O. Manzyuk).
[43] A∞-algebras, A∞-categories and A∞-functors, Handbook of Algebra, vol. 5,
Elsevier Science Publ., North Holland, 2008, pp. 143–188 (with O. Manzyuk).
[44] Homotopy unital A∞-algebras, J. Algebra 329 (2011), no. 1, 190–212,
Special Issue Celebrating the 60th Birthday of Corrado De Concini,
http://dx.doi.org/10.1016/j.jalgebra.2010.02.009
[45] Bar and cobar constructions for curved algebras and coalgebras,
Matematychni Studii 40 (2013), no. 2, 115–131.
[46] A∞-morphisms with several entries, Theory Appl. Categ. 30 (2015), no. 45,
1501–1551, http://www.tac.mta.ca/tac/volumes/30/45/30-45abs.html
[47] Homotopy unital A∞-morphisms with several entries, Theory Appl. Categ.
30 (2015), no. 46, 1552–1623,
http://www.tac.mta.ca/tac/volumes/30/46/30-46abs.html
[48] Homotopy cooperads, Математичнi Студiї 44 (2015), no. 2, 119–160,
http://matstud.org.ua/texts/2015/44_2/119-160.html
[49] Curved homotopy coalgebras, Appl. Categ. Structures 25 (2017), no. 6,
991–1036, https://doi.org/10.1007/s10485-016-9440-4
[50] Moyal and Rankin–Cohen deformations of algebras, Proc. Int. Geom. Cent. 11
(2018), no. 2, 48–52, https://doi.org/10.15673/tmgc.v11i2.1027
[51] Модельна структура на категоріях пов’язаних з категоріями комплексів,
Український математичний журнал 72 (2020), no. 2, 232–244,
http://umj.imath.kiev.ua/index.php/umj/article/view/682
Переклад в https://doi.org/10.1007/s11253-020-01780-3.
[52] Filtered cocategories, Theory Appl. Categ. 35 (2020), no. 47, 1726–1770,
http://www.tac.mta.ca/tac/volumes/35/47/35-47.pdf