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Representations and Cocycle Twists of Color Lie Algebras
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 .Comment: 18 pages, with an concrete exampl
Color Lie algebras and Lie algebras of order F
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
Let be a -Hopf algebra with bijection antipode and let be
a -graded -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 -module via the counit of ,
is the adjoint -module associated to the graded -bimodule
and denotes the -graded Hochschild cohomology. As an
application, we deduce that the cohomology of color Lie algebra is
isomorphic to the graded Hochschild cohomology of the universal enveloping
algebra , solving a question of M. Scheunert.Comment: 21 pages. To appear to Journal of Algebr
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