Cohomology of 3-dimensional color Lie algebras

Dmitri Piontkovski; Sergei Silvestrov

doi:10.1016/j.jalgebra.2006.11.008

Cohomology of 3-dimensional color Lie algebras

Dmitri Piontkovski, Sergei Silvestrov

Mathematics (Faculty of Engineering)

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	499-513
Journal	Journal of Algebra
Volume	316
Issue number	2
DOIs	https://doi.org/10.1016/j.jalgebra.2006.11.008
Publication status	Published - 2007

Subject classification (UKÄ)

Mathematics

Free keywords

color Lie algebras
Koszul algebras
quadratic algebras
cohomology

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10.1016/j.jalgebra.2006.11.008

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title = "Cohomology of 3-dimensional color Lie algebras",

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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AU - Piontkovski, Dmitri

AU - Silvestrov, Sergei

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N2 - 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.

AB - 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.

KW - color Lie algebras

KW - Koszul algebras

KW - quadratic algebras

KW - cohomology

U2 - 10.1016/j.jalgebra.2006.11.008

DO - 10.1016/j.jalgebra.2006.11.008

M3 - Article

SN - 0021-8693

VL - 316

SP - 499

EP - 513

JO - Journal of Algebra

JF - Journal of Algebra

IS - 2

ER -

Cohomology of 3-dimensional color Lie algebras

Abstract

Subject classification (UKÄ)

Free keywords

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