Note on The Cohomology of Color Hopf and Lie Algebras
| dc.creator | Chen, Xiao-Wu | |
| dc.creator | Petit, Toukaiddine | |
| dc.creator | Van Oystaeyen, Freddy | |
| dc.date | 2005-04-27 | |
| dc.date | 2005-12-01 | |
| dc.date.accessioned | 2026-07-07T06:38:37Z | |
| dc.date.available | 2026-07-07T06:38:37Z | |
| dc.description | Let $A$ 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.description | 21 pages. To appear to Journal of Algebra | |
| dc.identifier | https://arxiv.org/abs/math-ph/0504080 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0504080 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/100798 | |
| dc.subject | Mathematical Physics | |
| dc.subject | 13D07, 16W70 | |
| dc.title | Note on The Cohomology of Color Hopf and Lie Algebras | |
| dc.type | text |