Semigroup C⁎-algebras and amenability of semigroups

By Xin Li. 2011

155 citations recorded by the source corpus.

We construct reduced and full semigroup C⁎-algebras for left cancellative semigroups. Our new construction covers particular cases already considered by A. Nica and also Toeplitz algebras attached to rings of integers in number fields due to J. Cuntz. Moreover, we show how (left) amenability of semigroups can be expressed in terms of these semigroup C⁎-algebras in analogy to the group case.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8fbcbbe0033cb494f12714258c6309d7bb34be47

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In Algebra and Number Theory

In Mathematical Physics

Citations in the corpus

On C*-algebras associated to right LCM semigroups (2014, methodology): “Recall from [19] that for each right ideal X and p ∈ S, the sets pX = {px | x ∈ X} and pX = {y ∈ S | py ∈ X} are also right ideals.”
On the K-theory of crossed products by automorphic semigroup actions (2012, background): “The following definition is taken from [22] and plays an important rôle in [10, 23].”
Inverse Semigroup C*-Algebras Associated with Left Cancellative Semigroups (2012, background): “.5.7 since a cancellative left amenable Sembeds into the amenable group G(S). It remains to see that C∗ 0(Il(S)) is nuclear implies Sis left amenable. This was shown for Cs∗(S) in Proposition 4.17 in [17] with an argument analogous to the following: C∗(G(S)) is a quotient of C∗ 0(Il(S)) and is thus ”
On the K-theory of the C*-algebra generated by the left regular representation of an Ore semigroup (2012, background): “Li: School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London E1 4NS, United Kingdom; e-mail: xin.li@qmul.ac.uk Mathematics Subject Classification (2010): Primary 46L05, 46L80; Secondary 20Mxx, 11R04”
Partial transformation groupoids attached to graphs and semigroups (2016, methodology): “The key idea is that using partial transformation groupoids, we obtain structural results for our C*-algebras without assuming independence or the Toeplitz condition, which were crucial in our previous approach (see [19, 20]).”
Boundary quotients of C*-algebras of right LCM semigroups (2014, background): “). 1 1 Introduction A semigroup Pis left cancellative if pq= psimplies that q= s, and C*-algebras associated to such semigroups are an active topic of research in operator algebras. Li’s construction [Li12] of a C*-algebra C∗(P) from a left cancellative semigroup Pgeneralizes Nica’s quasilattice ord”