# The Structure and Represenation of a $C_{∗}$-Algebra Associated to the Super-Poincaré Group

### Keith C. Hannabuss

Balliol College, Oxford, UK### Winfried R.E. Weiss

University of Oxford, United Kingdom

## 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-Poincaré group, are then constructed by Takesaki's method. It is then shown that they may also be constructed by Rieffel's $C_{∗}$-algebraic induction. Tensor product decompositions are briefly discussed.

## Cite this article

Keith C. Hannabuss, Winfried R.E. Weiss, The Structure and Represenation of a $C_{∗}$-Algebra Associated to the Super-Poincaré Group. Publ. Res. Inst. Math. Sci. 26 (1990), no. 6, pp. 967–978

DOI 10.2977/PRIMS/1195170571