Cohomology of 3-dimensional color Lie algebras
classification
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math.RA
keywords
coloralgebraalgebrascohomologycomplexdimensionalkoszulsuperalgebras
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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 3-dimensional color Lie superalgebras.
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