Non-formal deformation quantization of abelian supergroups

Details Non-formal deformation quantization of abelian supergroups Non-formal deformation quantization of abelian supergroups

2011-08-19

arxiv.org/abs/1108.3947v1

Mathematics

Quantum Algebra

12 pages, Contribution to the proceedings of the EU-NCG 4th Annual Meeting on Noncommutative Geometry (Bucharest, April 2011)

Scientific paper

We review recent works concerning deformation quantization of abelian supergroups. Indeed, we expose the construction of an induced representation of the Heisenberg supergroup and an associated pseudodifferential calculus by using Kirillov's orbits method. Then, a star-product is built on the abelian supergroup R^{m|n} together with a universal deformation formula for its actions. Using topological Hopf algebras, we reformulate this deformation as a continuous twist on comodule-algebras. We also introduce the notion of C*-superalgebra which is natural and compatible with the deformation. Finally, we show some applications in supergeometry and theoretical physics.

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