تقرير
Inverse semigroups of separated graphs and associated algebras
| العنوان: | Inverse semigroups of separated graphs and associated algebras |
|---|---|
| المؤلفون: | Ara, Pere, Buss, Alcides, Costa, Ado Dalla |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Operator Algebras, Mathematics - Rings and Algebras, 46L55, 20M18 |
| الوصف: | In this paper we introduce an inverse semigroup $\mathcal{S}(E,C)$ associated to a separated graph $(E,C)$ and describe its internal structure. In particular we show that it is strongly $E^*$-unitary and can be realized as a partial semidirect product of the form $\mathcal{Y}\rtimes\mathbb{F}$ for a certain partial action of the free group $\mathbb{F}=\mathbb{F}(E^1)$ on the edges of $E$ on a semilattice $\mathcal{Y}$ realizing the idempotents of $\mathcal{S}(E,C)$. In addition we also describe the spectrum as well as the tight spectrum of $\mathcal{Y}$. We then use the inverse semigroup $\mathcal{S}(E,C)$ to describe several ''tame'' algebras associated to $(E,C)$, including its Cohn algebra, its Leavitt-path algebra, and analogues in the realm of $C^*$-algebras, like the tame $C^*$-algebra $\mathcal{O}(E,C)$ and its Toeplitz extension $\mathcal{T}(E,C)$, proving that these algebras are canonically isomorphic to certain algebras attached to $\mathcal{S}(E,C)$. Our structural results on $\mathcal{S}(E,C)$ will then imply certain natural structure results for these algebras, like their description as partial crossed products. Comment: 45 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2403.05295 |
| رقم الأكسشن: | edsarx.2403.05295 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |