Abstract
AbstractA 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.
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More From: Mathematical Proceedings of the Cambridge Philosophical Society
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