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Cohomology of 3-dimensional color Lie algebras

Piontkovski, Dmitri and Silvestrov, Sergei LU (2007) In Journal of Algebra 316(2). p.499-513
Abstract
We develop the cohomology theory of color Lie algebras due to Scheunert-Zhang in a framework of non-homogeneous quadratic Koszul algebras. In this approach, the Chevalley-Eilenberg complex of a color Lie algebra becomes a standard Koszul complex for its universal enveloping algebra, providing a constructive method for computation of cohomology. As an application, we compute cohomologies with trivial coefficients of Z(2)(n)-graded 3-dimensional color Lie algebras. 2 (c) 2006 Elsevier Inc. All rights reserved.
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
color Lie algebras, Koszul algebras, quadratic algebras, cohomology
in
Journal of Algebra
volume
316
issue
2
pages
499 - 513
publisher
Elsevier
external identifiers
  • wos:000250532000002
  • scopus:34548698904
ISSN
0021-8693
DOI
10.1016/j.jalgebra.2006.11.008
language
English
LU publication?
yes
id
ff016007-4564-46b1-a02d-c062a7e10688 (old id 653119)
date added to LUP
2007-12-18 17:20:05
date last changed
2017-01-29 03:27:45
@article{ff016007-4564-46b1-a02d-c062a7e10688,
  abstract     = {We develop the cohomology theory of color Lie algebras due to Scheunert-Zhang in a framework of non-homogeneous quadratic Koszul algebras. In this approach, the Chevalley-Eilenberg complex of a color Lie algebra becomes a standard Koszul complex for its universal enveloping algebra, providing a constructive method for computation of cohomology. As an application, we compute cohomologies with trivial coefficients of Z(2)(n)-graded 3-dimensional color Lie algebras. 2 (c) 2006 Elsevier Inc. All rights reserved.},
  author       = {Piontkovski, Dmitri and Silvestrov, Sergei},
  issn         = {0021-8693},
  keyword      = {color Lie algebras,Koszul algebras,quadratic algebras,cohomology},
  language     = {eng},
  number       = {2},
  pages        = {499--513},
  publisher    = {Elsevier},
  series       = {Journal of Algebra},
  title        = {Cohomology of 3-dimensional color Lie algebras},
  url          = {http://dx.doi.org/10.1016/j.jalgebra.2006.11.008},
  volume       = {316},
  year         = {2007},
}