2022/02/18 by Banerjee, Bikram, Mukherjee, Goutam
#15A66 #16E40 #16S80 #Algebraic Topology (math.AT) #FOS: Mathematics
paper · doi:10.48550/arxiv.2202.09065
In this article we construct a cochain complex of a complex Clifford algebra with coefficients in itself in a combinatorial fashion and we call the corresponding cohomology by \it Clifford cohomology. We show that \it Clifford cohomology controls the deformation of a complex Clifford algebra and can classify them up to Morita equivalence. We also study Hochschild cohomology groups and formal deformations of the algebra of smooth sections of a complex Clifford algebra bundle over an even dimensional orientable Riemannian manifold \(M\) which admits a \(Spinc\) structure.