Representations and cocycle twists of color Lie algebras

X. -W. Chen; Sergei Silvestrov; F. Van Oystaeyen

doi:10.1007/s10468-006-9027-0

Representations and cocycle twists of color Lie algebras

X. -W. Chen, Sergei Silvestrov, F. Van Oystaeyen

Mathematics (Faculty of Engineering)

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

Abstract

We study relations between finite-dimensional representations of color Lie algebras and their cocycle twists. Main tools are the universal enveloping algebras and their FCR-properties (finite-dimensional representations are completely reducible.) Cocycle twist preserves the FCR-property. As an application, we compute all finite dimensional representations (up to isomorphism) of the color Lie algebra sl(2)(c).

Original language	English
Pages (from-to)	633-650
Journal	Algebras and Representation Theory
Volume	9
Issue number	6
DOIs	https://doi.org/10.1007/s10468-006-9027-0
Publication status	Published - 2006

Subject classification (UKÄ)

Mathematics

Free keywords

color Lie algebras
cocycle twists
FCR-algebras

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10.1007/s10468-006-9027-0

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title = "Representations and cocycle twists of color Lie algebras",

abstract = "We study relations between finite-dimensional representations of color Lie algebras and their cocycle twists. Main tools are the universal enveloping algebras and their FCR-properties (finite-dimensional representations are completely reducible.) Cocycle twist preserves the FCR-property. As an application, we compute all finite dimensional representations (up to isomorphism) of the color Lie algebra sl(2)(c).",

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T1 - Representations and cocycle twists of color Lie algebras

AU - Chen, X. -W.

AU - Silvestrov, Sergei

AU - Van Oystaeyen, F.

PY - 2006

Y1 - 2006

N2 - We study relations between finite-dimensional representations of color Lie algebras and their cocycle twists. Main tools are the universal enveloping algebras and their FCR-properties (finite-dimensional representations are completely reducible.) Cocycle twist preserves the FCR-property. As an application, we compute all finite dimensional representations (up to isomorphism) of the color Lie algebra sl(2)(c).

AB - We study relations between finite-dimensional representations of color Lie algebras and their cocycle twists. Main tools are the universal enveloping algebras and their FCR-properties (finite-dimensional representations are completely reducible.) Cocycle twist preserves the FCR-property. As an application, we compute all finite dimensional representations (up to isomorphism) of the color Lie algebra sl(2)(c).

KW - color Lie algebras

KW - cocycle twists

KW - FCR-algebras

U2 - 10.1007/s10468-006-9027-0

DO - 10.1007/s10468-006-9027-0

M3 - Article

SN - 1386-923X

VL - 9

SP - 633

EP - 650

JO - Algebras and Representation Theory

JF - Algebras and Representation Theory

IS - 6

ER -

Representations and cocycle twists of color Lie algebras

Abstract

Subject classification (UKÄ)

Free keywords

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