Note on the cohomology of color Hopf and Lie algebras
نویسندگان
چکیده
Let A be a (G,χ)-Hopf algebra with bijective antipode and let M be a G-graded A-bimodule. We prove that there exists an isomorphism HH∗gr(A,M)∼= Ext∗A-gr ( K,ad (M) ) , where K is viewed as the trivial graded A-module via the counit of A, adM is the adjoint A-module associated to the graded A-bimodule M and HH∗gr denotes the G-graded Hochschild cohomology. As an application, we deduce that the graded cohomology of color Lie algebra L is isomorphic to the graded Hochschild cohomology of its universal enveloping algebra U(L), solving a question of M. Scheunert. © 2005 Elsevier Inc. All rights reserved. * Corresponding author. E-mail addresses: [email protected] (X.-W. Chen), [email protected] (T. Petit), [email protected] (F. Van Oystaeyen). 1 Supported by National Natural Science Foundation of China (No. 10501041) and AsiaLink project “Algebras and Representations in China and Europe” ASI/B7-301/98/679-11. 2 Supported by the ESF Scientific Programme “NOG.” 3 Supported by the EC project Liegrits MCRTN 505078. 0021-8693/$ – see front matter © 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.jalgebra.2005.11.026 420 X.-W. Chen et al. / Journal of Algebra 299 (2006) 419–442
منابع مشابه
Note on Cohomology of Color Hopf and Lie Algebras
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 HH∗gr(A,M) ∼= Ext ∗ A-gr(K, (M)), where K is viewed as the trivial graded A-module via the counit of A, M is the adjoint A-module associated to the graded A-bimodule M and HHgr denotes the G-graded Hochschild cohomology. As an application, we deduce that the cohom...
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