Cohomology of 3-dimensional color Lie algebras
نویسندگان
چکیده
منابع مشابه
Cohomology of 3-dimensional Color Lie Algebras
We develop the cohomology theory of color Lie superalgebras due to Scheunert–Zhang in a framework of nonhomogeneous quadratic Koszul algebras. In this approach, the Chevalley– Eilenberg complex of a color Lie algebra becomes a standard Koszul complex for its universal enveloping algebra. As an application, we calculate cohomologies with trivial coefficients of Zn 2 – graded 3–dimensional color ...
متن کاملNote 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...
متن کاملNote on the cohomology of color Hopf and Lie algebras
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 ...
متن کاملCohomology of Lie groups and Lie algebras
The aim of this expository essay is to illustrate one example of a local-to-global phenomenon. What we mean by that is better illustrated by explaining the topic at hand. We aim to understand the de Rham cohomology groups of a Lie group. But instead of doing it using actual differential forms, we shall use the properties of a Lie group (especially the fact that it is a group) to reduce calculat...
متن کاملSemiinfinite Cohomology of Lie-* Algebras
This paper is a natural extension of the previous note [Ar2]. Semiinfinite cohomology of Tate Lie algebra was defined in that note in terms of some duality resembling Koszul duality. The language of differential graded Lie algebroids was the main technical tool of the note. The present note is devoted to globalization of the main construction from [Ar2] in the following sense. The setup in [Ar2...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2007
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2006.11.008