An inverse semigroup approach to self-similar k-graph $C^*$-algebras and simplicity

Hossein Larki

An inverse semigroup approach to self-similar k-graph $C^*$-algebras and simplicity

Operator Algebras 2024-11-22 v1

Authors: Hossein Larki

Abstract

We generalize the Li-Yang notion of self-similar $k$ -graph $(G,\Lambda)$ and its $C^*$ -algebra $\mathcal{O}_{G,\Lambda}$ to any finitely aligned $k$ -graph $\Lambda$ . We then introduce an inverse semigroup model for $\mathcal{O}_{G,\Lambda}$ and analyze its tight groupoid and $C^*$ -algebra via inverse semigroup methods.

Keywords

inverse semigroup self-similar k-graph C*-algebra tight groupoid simplicity

Cite

@article{arxiv.2411.14027,
  title  = {An inverse semigroup approach to self-similar k-graph $C^*$-algebras and simplicity},
  author = {Hossein Larki},
  journal= {arXiv preprint arXiv:2411.14027},
  year   = {2024}
}

Comments

38 pages

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