Clifford algebras as superalgebras and quantization
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.
Lie superalgebra of differential operators
scientific article; zbMATH DE number 3912574