Clifford algebras as superalgebras and quantization
type: Item
instance of: scholarly article
title: Clifford algebras as superalgebras and quantization
zbMATH Open document ID: 0572.17002
DOI: 10.1007/BF01017920
published in: Theoretical and Mathematical Physics
publication date: 1984-01-01T00:00:00Z
review text: On supermanifolds there are two types of mechanics, to which there correspond superalgebras of functions with Poisson or Buttin brackets (respectively, antibrackets). For them, quantizations are constructed in the following senses: 1) representations of the commutation relations, 2) deformation of the Poisson (respectively, Buttin) superalgebra into the Lie superalgebra of differential operators, 3) analogs of the spinor representation of a symplectic (orthogonal) Lie algebra. The Clifford algebra is given a new interpretation. Invariant polynomials and Casimir operators on the Poisson superalgebra are described.
Mathematics Subject Classification ID: 17B63
Mathematics Subject Classification ID: 53D50
Mathematics Subject Classification ID: 15A72
Mathematics Subject Classification ID: 81R10
Mathematics Subject Classification ID: 58A50
zbMATH DE Number: 3912574
zbMATH Keywords: Clifford superalgebra
zbMATH Keywords: Poisson superalgebra
zbMATH Keywords: Buttin superalgebra
zbMATH Keywords: Buttin brackets
zbMATH Keywords: quantizations
zbMATH Keywords: Lie superalgebra of differential operators
author: Dimitry Leites
MaRDI profile type: Publication
cites work: Graded Lie algebras in mathematics and physics (Bose-Fermi symmetry)
cites work: Lie superalgebras
cites work: Quantization and commutative superalgebras
cites work: Two constructions of affine Lie algebra representations and boson-fermion correspondence in quantum field theory
full work available at URL: https://doi.org/10.1007/bf01017920
OpenAlex ID: W2040865771
description: scientific article; zbMATH DE number 3912574