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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
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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
2016-04-01 11:55:51
date last changed
2022-03-28 17:50:15
@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}},
  keywords     = {{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}},
  doi          = {{10.1016/j.jalgebra.2006.11.008}},
  volume       = {{316}},
  year         = {{2007}},
}