Algebra Seminar

The de Rham cohomology of a smooth manifold roughly measures the failure of the fundamental theorem of calculus on such a manifold. When such a manifold is a compact homogenous space $G/R$ this cohomology can be calculated via a differential graded algebra in the  exterior powers of its cotangent space $Lie(G)/Lie(R)^*$. When this exterior algebra is replaced by a Clifford algebra, one creates a filtered deformation of de Rham cohomology, which we call Clifford cohomology. I will explain this theory and give results on the description of this cohomology and provide links to Dirac cohomology and nilpotent Lie algebra cohomology. Joint work with Karmen Grizelj, Andrey Krutov, Kyo Nishiyama and Pavle Pandzic.

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