Cohomology of 3-dimensional color Lie algebras
(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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/653119
- author
- Piontkovski, Dmitri and Silvestrov, Sergei LU
- organization
- publishing date
- 2007
- 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}}, }