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On Operator Algebras Associated with Monomial Ideals in Noncommuting Variables by Kakariadis, Evgenios T. A.; Shalit, Orr M. is a scholarly article available to read on EtoBox.

What is On Operator Algebras Associated with Monomial Ideals in Noncommuting Variables about?

We study operator algebras arising from monomial ideals in the ring of polynomials in noncommuting variables, through the apparatus of subproduct systems and C*-correspondences. We provide a full comparison amongst the related operator algebras. For our analysis we isolate a partially defined dynamical system, to which we refer as the {\em quantised dynamics} of the monomial ideal. In addition we revisit several previously considered constructions. These include Matsumoto's subshift C*-algebras, as well as the tensor and the Pimsner algebras associated with dynamical systems or graphs. We sort out the various relations by giving concrete conditions and counterexamples that orientate the operator algebras of our context. It appears that the boundary C*-algebras do not arise as the quotient with the compact operators unconditionally. We establish a dichotomy to this effect by examining the resulting tensor algebras. We identify their boundary representations, we analyse their C*-envelopes, and we give criteria for hyperrigidity. Moreover we completely classify them in terms of the data provided by the monomial ideals. For tensor algebras of C*-correspondences and bounded isomorphisms

Author

Kakariadis, Evgenios T. A.; Shalit, Orr M.

Published

2015

Language

EN