Semicrossed Products of Operator Algebras: A Survey
Kenneth R. Davidson, Adam H. Fuller, Evgenios T.A. Kakariadis
TL;DR
This survey reviews the development and recent advances in semicrossed product algebras, highlighting their applications in dynamical systems, conjugacy problems, dilation theory, and C*-envelopes.
Contribution
It provides a comprehensive overview of the history, key concepts, and recent research directions in semicrossed product algebras for operator algebras.
Findings
Summarizes the role of semicrossed products in dynamical systems
Discusses recent progress on conjugacy and dilation problems
Explores connections to C*-envelopes and dynamics
Abstract
Semicrossed product algebras have been used to study dynamical systems since their introduction by Arveson in 1967. In this survey article, we discuss the history and some recent work, focussing on the conjugacy problem, dilation theory and C*-envelopes, and some connections back to the dynamics
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Taxonomy
TopicsAdvanced Topics in Algebra · Advanced Algebra and Logic · Algebraic structures and combinatorial models