5,395 research outputs found

    Representations and Cocycle Twists of Color Lie Algebras

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    We study relations between finite-dimensional representations of color Lie algebras and their cocycle twists. Main tools are the universal enveloping algebras and their FCR-properties (finite-dimensional representations are completely reducible.) Cocycle twist preserves the FCR-property. As an application, we compute all finite dimensional representations (up to isomorphism) of the color Lie algebra sl2csl_2^c.Comment: 18 pages, with an concrete exampl

    Color Lie algebras and Lie algebras of order F

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    The notion of color algebras is generalized to the class of F-ary algebras, and corresponding decoloration theorems are established. This is used to give a construction of colored structures by means of tensor products with Clifford-like algebras. It is moreover shown that color algebras admit realisations as q=0 quon algebras.Comment: LaTeX, 16 page

    Note on The Cohomology of Color Hopf and Lie Algebras

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    Let AA be a (G,Ο‡)(G, \chi)-Hopf algebra with bijection antipode and let MM be a GG-graded AA-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 AA-module via the counit of AA, adM^{ad} M is the adjoint AA-module associated to the graded AA-bimodule MM and HHgr\mathrm{HH}_{\rm gr} denotes the GG-graded Hochschild cohomology. As an application, we deduce that the cohomology of color Lie algebra LL is isomorphic to the graded Hochschild cohomology of the universal enveloping algebra U(L)U(L), solving a question of M. Scheunert.Comment: 21 pages. To appear to Journal of Algebr
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