Non-formal deformation quantization of abelian supergroups
(2012) EU - NCG 4th Annual Meeting — Location: Bucharest, Romania (25.April.2011)
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- Abstract
- 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 Rm|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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Marcillaud de Goursac, A. (2012). Non-formal deformation quantization of abelian supergroups. Theta Series in Advanced Mathematics, 15(1), 61-73. https://hdl.handle.net/2078.5/69348 (Original work published 2012)