Noncommutative Supergeometry and Quantum Supergroups
Axel de Goursac
TL;DR
This paper reviews noncommutative supergeometry concepts like Hilbert superspaces and quantum supergroups, highlighting their applications in harmonic analysis, deformation quantization, and quantum field theory on noncommutative spaces.
Contribution
It provides a comprehensive overview of noncommutative supergeometry and introduces explicit examples such as deformed superspaces and quantum supergroups.
Findings
Applications in harmonic analysis of Lie supergroups
Non-formal deformation quantization of supermanifolds
Explicit examples of quantum supergroups and noncommutative supertori
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.
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