Inverse Semigroup C*-Algebras Associated with Left Cancellative Semigroups

By M. Norling. Proceedings of the Edinburgh Mathematical Society, 2012

49 citations recorded by the source corpus.

Abstract To each discrete left cancellative semigroup S one may associate an inverse semigroup Il(S), often called the left inverse hull of S. We show how the full and reduced C*-algebras of Il(S) are related to the full and reduced semigroup C*-algebras for S, recently introduced by Li, and give conditions ensuring that these algebras are isomorphic. Our picture provides an enhanced understanding of Li's algebras.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/0e96719a6135a3cda840798498382598a4e9b763

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Nathan Brownlowe
2. Nadia S. Larsen
3. Nicolai Stammeier
4. Charles Starling
5. Xin Li

In Computational Theory and Mathematics

1. Charles Starling
2. Nathan Brownlowe
3. Nadia S. Larsen
4. Xin Li
5. Nicolai Stammeier

In Mathematical Physics

1. Charles Starling
2. Nathan Brownlowe
3. Nadia S. Larsen
4. Nicolai Stammeier
5. Xin Li
6. J. Cuntz
7. S. Echterhoff
8. Mikhailo Dokuchaev

Citations in the corpus

• Partial transformation groupoids attached to graphs and semigroups (2016, background): “Note that the statement in the last corollary was also obtained in [31].”
• Nuclearity of semigroup C*-algebras and the connection to amenability (2012, methodology): “the following converse of Proposition 4.17 in [Li2]: Corollary 6.7. If P is cancellative, left amenable and if Jis independent, then C∗ s(P) is nuclear. This result was also obtained independently in [Nor] using different methods. 7. Ideals induced from invariant spectral subsets In this section, we ”
• On C*-algebras associated to right LCM semigroups (2014, methodology): “o certain relations which are imposed by the regular representation. For certain classes of semigroups, the canonical isomorphism between the full and reduced semigroup C∗-algebras was established in [19, 20, 27]. In [2], the authors studied the full semigroup C∗-algebra arising from an algebraic co”
• Boundary quotients of C*-algebras of right LCM semigroups (2014, methodology): “s such that two principal right ideals are either disjoint or intersect in another principal right ideal) and calls these CRM monoids (named for Clifford, Reilly and McAlister). In other works such as [Nor14], such semigroups are said to satisfy Clifford’s condition. Let P be a right LCM semigroup wit”