Noncommutative Supergeometry and Quantum Supergroups

Abstract

This is a review of concepts of noncommutative supergeometry - namely Hilbert superspace, C*-superalgebra, quantum supergroup - and corresponding results. In particular, we present applications of noncommutative supergeometry in harmonic analysis of Lie supergroups, non-formal deformation quantization of supermanifolds, quantum field theory on noncommutative spaces; and we give explicit examples such as deformation of flat superspaces, noncommutative supertori, solvable topological quantum supergroups.

12 pages, Proceedings of the 30th International Colloquium on Group Theoretical Methods in Physics (Ghent, July 2014)

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