Lyubashenko Volodymyr
Publications
Monographs
[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).
Articles
[1] Boundary values of solutions of differential–operator equations, Dopovıdı
Akad. Nauk Ukraın. RSR Ser. A (1984), no. 4, 71–73 (with A. G. Reznikov).
[2] The Berezinian in some monoidal categories, Ukrainian Math. J. 38 (1986),
no. 5, 501–505.
[3] Hopf algebras and vector symmetries, Sov. Math. Surveys, 41 (1986), no. 5,
153–154, Uspekhi Mat. Nauk 41 (1986), no. 5, 185–186.
[4] Superanalysis and solutions to the triangles equation, Ph.D. thesis,
Institute for Mathematics, Kyiv, 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] Example of a triangulated Hopf category, Vısnik Kiıv Unıv Ser. Fız.-Mat.
Nauki (1999), no. 2, 50–58, in Ukrainian.
[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] Tensor product of equivariant perverse sheaves, Vısnik Kiıv Unıv. Ser.
Fız.-Mat. Nauki (2000), no. 2, 22–34, in Ukrainian.
[24] Coherence isomorphisms for triangulated Hopf category SL(2), Naukovi
zapysky of Kyiv-Mohyla academy (Physical-mathematical sciences) 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] Squared Hopf algebras and the modular functor, Kyiv National Taras
Shevchenko University, Doctor of sciences in physics and mathematics
thesis, Kyiv, December 2000.
[27] External tensor product of perverse sheaves, Ukr. Math. J. 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, Proc. 3rd
Internat. Alg. Conf. in Ukraine, July 2-8 (Sumy) 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, Naukovi zapysky of
Kyiv-Mohyla academy (Physical-mathematical sciences) 21 (2003), 5–20
(with S. A. Ovsienko).
[35] Special PROPs and homotopy bialgebras, Math. bulletin of the Shevchenko
Sci. Soc. 1 (2004), 59–76, in Ukrainian.
[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, Problems of topology and related questions
(V. V. Sharko, ed.), Proc. of Inst. of Mathematics NASU, vol. 3, no. 3,
Inst. of Mathematics, Nat. Acad. Sci. Ukraine, Kyiv, 2006, 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, Matematychni Studii 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] A model structure on categories related to categories of complexes, Ukr.
Math. J. 72 (2020), no. 2, 232–244,
http://umj.imath.kiev.ua/index.php/umj/article/view/682
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).
Articles
[1] Boundary values of solutions of differential–operator equations, Dopovıdı
Akad. Nauk Ukraın. RSR Ser. A (1984), no. 4, 71–73 (with A. G. Reznikov).
[2] The Berezinian in some monoidal categories, Ukrainian Math. J. 38 (1986),
no. 5, 501–505.
[3] Hopf algebras and vector symmetries, Sov. Math. Surveys, 41 (1986), no. 5,
153–154, Uspekhi Mat. Nauk 41 (1986), no. 5, 185–186.
[4] Superanalysis and solutions to the triangles equation, Ph.D. thesis,
Institute for Mathematics, Kyiv, 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] Example of a triangulated Hopf category, Vısnik Kiıv Unıv Ser. Fız.-Mat.
Nauki (1999), no. 2, 50–58, in Ukrainian.
[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] Tensor product of equivariant perverse sheaves, Vısnik Kiıv Unıv. Ser.
Fız.-Mat. Nauki (2000), no. 2, 22–34, in Ukrainian.
[24] Coherence isomorphisms for triangulated Hopf category SL(2), Naukovi
zapysky of Kyiv-Mohyla academy (Physical-mathematical sciences) 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] Squared Hopf algebras and the modular functor, Kyiv National Taras
Shevchenko University, Doctor of sciences in physics and mathematics
thesis, Kyiv, December 2000.
[27] External tensor product of perverse sheaves, Ukr. Math. J. 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, Proc. 3rd
Internat. Alg. Conf. in Ukraine, July 2-8 (Sumy) 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, Naukovi zapysky of
Kyiv-Mohyla academy (Physical-mathematical sciences) 21 (2003), 5–20
(with S. A. Ovsienko).
[35] Special PROPs and homotopy bialgebras, Math. bulletin of the Shevchenko
Sci. Soc. 1 (2004), 59–76, in Ukrainian.
[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, Problems of topology and related questions
(V. V. Sharko, ed.), Proc. of Inst. of Mathematics NASU, vol. 3, no. 3,
Inst. of Mathematics, Nat. Acad. Sci. Ukraine, Kyiv, 2006, 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, Matematychni Studii 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] A model structure on categories related to categories of complexes, Ukr.
Math. J. 72 (2020), no. 2, 232–244,
http://umj.imath.kiev.ua/index.php/umj/article/view/682
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