2005/08/29 by Dmitri Piontkovski, Piontkovski, Dmitri, Sergei Silvestrov +1
Mathematics · #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Cohomology #Geometry #Graded Lie algebra #Homotopy and Cohomology in Algebraic Topology #Lie algebra #Lie conformal algebra #Mathematics #Pure mathematics #Quadratic equation #math.KT #math.RA #msc:16S37 #msc:17B56 #msc:17B75
paper · pdf · doi:10.48550/arxiv.math/0508573
openalex publication_date 2005/08/29 · arxiv created 2009/11/29 · arxiv updated 2009/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.