Spherical representations of $C^{\ast }$-flows I

Abstract

We propose an abstract framework of a kind of representation theory for $C^{\ast }$-flows, i.e., $C^{\ast }$-algebras equipped with one-parameter automorphism groups, as a proper generalization of Olshanski's formalism of unitary representation theory for infinite-dimensional groups such as the infinite-dimensional unitary group $\mathrm{U}(\infty )$. The present framework, in particular, clarifies some overlaps and/or similarities between a certain unitary representation theory of infinite-dimensional groups and existing works in operator algebras, and captures arbitrary projective chains arising from links.

arXiv commenttypos corrected; a sequel to this paper is arXiv:2201.10931

Cited by in corpus (1)

• Spherical Representations of $C^{\ast }$-Flows II: Representation System and Quantum Group Setup