|
SIGMA 9 (2013), 063, 10 pages arXiv:1201.5071
https://doi.org/10.3842/SIGMA.2013.063
Contribution to the Special Issue on New Directions in Lie Theory
Leibniz Algebras and Lie Algebras
Geoffrey Mason a and Gaywalee Yamskulna b, c
a) Department of Mathematics, University of California, Santa Cruz, CA 95064, USA
b) Department of Mathematical Sciences, Illinois State University, Normal, IL 61790, USA
c) Institute of Science, Walailak University, Nakon Si Thammarat, Thailand
Received September 09, 2013, in final form October 19, 2013; Published online October 23, 2013
Abstract
This paper concerns the algebraic structure of
finite-dimensional complex Leibniz algebras. In
particular, we introduce left central and symmetric
Leibniz algebras, and study the poset of Lie subalgebras
using an associative bilinear pairing taking values
in the Leibniz kernel.
Key words:
Leibniz algebras; Lie algebras.
pdf (312 kb)
tex (16 kb)
References
- Ayupov Sh.A., Omirov B.A., On Leibniz algebras, in Algebra and Operator Theory
(Tashkent, 1997), Kluwer Acad. Publ., Dordrecht, 1998, 1-12.
- Barnes D.W., On Engel's theorem for Leibniz algebras, Comm.
Algebra 40 (2012), 1388-1389, arXiv:1012.0608.
- Barnes D.W., On Levi's theorem for Leibniz algebras, Bull. Aust.
Math. Soc. 86 (2012), 184-185, arXiv:1109.1060.
- Lepowsky J., Li H., Introduction to vertex operator algebras and their
representations, Progress in Mathematics, Vol. 227, Birkhäuser
Boston Inc., Boston, MA, 2004.
- Loday J.L., Une version non commutative des algèbres de Lie: les algèbres
de Leibniz, Enseign. Math. 39 (1993), 269-293.
- Loday J.L., Cyclic homology, Grundlehren der Mathematischen
Wissenschaften, Vol. 301, 2nd ed., Springer-Verlag, Berlin, 1998.
- Mason G., Yamskulna G., On the structure of N-graded vertex operator
algebras, arXiv:1310.0545.
|
|