Super Toeplitz operators and non-perturbative deformation quantization of supermanifolds
type: Item
instance of: scholarly article
title: Super Toeplitz operators and non-perturbative deformation quantization of supermanifolds
zbMATH Open document ID: 0791.58012
DOI: 10.1007/BF02099040
author: David Borthwick
author: Andrzej Leśniewski
author: M. Rinaldi
author: Slawomir Klimek
published in: Communications in Mathematical Physics
publication date: 1993-06-29T00:00:00Z
review text: In the paper under review super Toeplitz operators are used to construct quantization deformations of the algebras of functions on complex supermanifolds. The resulting algebras may be regarded as algebras of ``quantized functions'' in the sense of Connes's noncommutative geometry. The semi-classical limits of these deformations correspond to super Poisson structures. The paper does not develop a general theory, but rather deals with two specific examples, namely, the trivial (1,1) dimensional supermanifold over the unit disk in \(\mathbb{C}\), and the trivial \((m,n)\) dimensional supermanifold based on \(\mathbb{C}^ m\).
Mathematics Subject Classification ID: 46L85
Mathematics Subject Classification ID: 46L87
Mathematics Subject Classification ID: 47B35
Mathematics Subject Classification ID: 58A50
zbMATH DE Number: 221171
zbMATH Keywords: noncommutative differential geometry
zbMATH Keywords: super Toeplitz operators
zbMATH Keywords: quantization deformations
zbMATH Keywords: supermanifolds
reviewed by: Ugo Bruzzo
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02099040
OpenAlex ID: W2043928589
description: scientific article; zbMATH DE number 221171