English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this exposition we highlight product systems as the semigroup analogue ofFell bundles. Motivated by Fock creation operators we extend the definition ofFowler's product systems over unital discrete left-cancellative semigroups, viaboth a concrete and an abstract characterization. We next underline theimportance of Fock spaces and Fell bundle methods for obtaining covariantrepresentation results. First, the strongly covariant representations ofSehnem, for product systems over group embeddable semigroups, find theiranalogue here. Secondly, we give two solutions for the existence of theco-universal C*-algebra with respect to equivariant injective Fock-covariantrepresentations in this context. The first one uses an intertwining isometrytechnique to realize it as the C*-envelope of the normal cosystem on the Focktensor algebra. The second uses a Fell bundle quotient technique to realize itas the reduced C*-algebra of Sehnem's strong covariance relations. ThisC*-algebra is boundary for a larger class of equivariant injectiverepresentations.

Product systems and their representations: an approach using Fock spaces and Fell bundles