gautesc

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Academic interests

Dynamical entropy, Semigroup C*-algebras.

Tags: Mathematics, Operator Algebra, Entropy, Sofic Groups.

Neshveyev, Sergey & Schwartz, Gaute (2023). Non-Hausdorff etale groupoids and C*-algebras of left cancellative monoids. Münster Journal of Mathematics. ISSN 1867-5778. 16(1), p. 147–175. doi: 10.17879/51009604279. Full text in Research Archive

Schwartz, Gaute (2025). The C∗-algebras of Left Cancellative Monoids via Étale Groupoids. Universitetet i Oslo. Full text in Research Archive Show summary
Schwartz investigates how C*-algebras arising from monoids can be described by groupoids. Monoids form a very general class of algebraic structures whereas groupoids are more tangible to work with. Relating a groupoid to the monoid is therefore desirable. Technical difficulties arise when the topology of the groupoid is non-Hausdorff. This means that there are distinct points of the groupoid which are inseparably near; using only the topology it is impossible to keep these points apart. By leveraging the interplay between monoids and groupoids we are nevertheless able to give combinatorial properties on the monoid which guarantee that the topology of the groupoid is not "too bad". Therefore, we are successful in describing the C*-algebras of even quite exotic monoids in terms of groupoids.

Published Sep. 25, 2020 2:22 PM - Last modified Sep. 29, 2021 4:40 PM