Note on The Cohomology of Color Hopf and Lie Algebras
Chen, Xiao-Wu ; Petit, Toukaiddine ; Van Oystaeyen, Freddy
arXiv, 0504080 / Harvested from arXiv
Text on arXiv
Let $A$ be a $(G, \chi)$-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.
Publié le : 2005-04-27
Classification:  Mathematical Physics,  13D07, 16W70 
@article{0504080,
     author = {Chen, Xiao-Wu and Petit, Toukaiddine and Van Oystaeyen, Freddy},
     title = {Note on The Cohomology of Color Hopf and Lie Algebras},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0504080}
}

Chen, Xiao-Wu; Petit, Toukaiddine; Van Oystaeyen, Freddy. Note on The Cohomology of Color Hopf and Lie Algebras. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0504080/