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A class of representations of involutive bialgebras

Published online by Cambridge University Press:  24 October 2008

Michael Schürmann
Michael Schürmann
Affiliation:
Institut für Angewandte Mathematik, Universität Heidelberg, Im Neuenheimer Feld 294, D-6900 Heidelberg 1, West Germany
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Abstract

A class of representations on Fock space is associated to a representation of the *-algebra structure of a cocommutative graded bialgebra with an involution. We prove that the Gelfand–Naimark–Segal (GNS) representation given by the convolution exponential of a conditionally positive linear functional can be embedded into a representation of this class. Our theory generalizes a well-known construction for infinitely divisible positive definite functions on a group. Applying our general result, we obtain a complete characterization of the GNS representations given by infinitely divisible states on involutive Lie superalgebras.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 107 , Issue 1 , January 1990 , pp. 149 - 175
Copyright
Copyright © Cambridge Philosophical Society 1990

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