Note on The Cohomology of Color Hopf and Lie Algebras

dc.creatorChen, Xiao-Wu
dc.creatorPetit, Toukaiddine
dc.creatorVan Oystaeyen, Freddy
dc.date2005-04-27
dc.date2005-12-01
dc.date.accessioned2026-07-07T06:38:37Z
dc.date.available2026-07-07T06:38:37Z
dc.descriptionLet $A$ be a $(G, χ)$-Hopf algebra with bijection antipode and let $M$ be a $G$-graded $A$-bimodule. We prove that there exists an isomorphism \mathrm{HH}^*_{\rm gr}(A, M)\cong{\rm Ext}^*_{A{-}{\rm gr}} (\K, {^{ad}(M)}), where $\K$ is viewed as the trivial graded $A$-module via the counit of $A$, $^{ad} M$ is the adjoint $A$-module associated to the graded $A$-bimodule $M$ and $\mathrm{HH}_{\rm gr}$ denotes the $G$-graded Hochschild cohomology. As an application, we deduce that the cohomology of color Lie algebra $L$ is isomorphic to the graded Hochschild cohomology of the universal enveloping algebra $U(L)$, solving a question of M. Scheunert.
dc.description21 pages. To appear to Journal of Algebra
dc.identifierhttps://arxiv.org/abs/math-ph/0504080
dc.identifierhttp://arxiv.org/abs/math-ph/0504080
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/100798
dc.subjectMathematical Physics
dc.subject13D07, 16W70
dc.titleNote on The Cohomology of Color Hopf and Lie Algebras
dc.typetext

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