The Structure and Represenation of a $\mathrm C^*$-Algebra Associated to the Super-Poincaré Group

Abstract

The representation theory of a class of algebras associated to certain graded Lie groups is investigated. To a group whose even part is central is associated a natural involutive algebra all of whose •-representations factor through a quotient algebra of continuous Clifford algebra-valued fields. The irreducible representations of crossed products of the algebra by a Lie algebra, such as the super-Poincare group, are then constructed by Takesaki's method. It is shown that they may also be constructed by Rieffel's C•-algebraic induction. Tensor decompositions are briefly discussed