Leavitt path algebras, Steinberg algebras and partial actions
About homological algebra of modules, the Tor and Ext functors and conjectures
Introduction to cyclic codes over commutative rings and algebraic integer numbers ...
| Full text | |
| Author(s): |
Tran Giang Nam
;
Zumbraegel, Jens
Total Authors: 2
|
| Document type: | Journal article |
| Source: | Journal of Pure and Applied Algebra; v. 225, n. 4, p. 22-pg., 2021-04-01. |
| Abstract | |
We investigate the algebra of a Hausdorff ample groupoid, introduced by Steinberg, over a commutative semiring S. In particular, we obtain a complete characterization of congruence-simpleness for such Steinberg algebras, extending the well-known characterizations when S is a field or a commutative ring. We also provide a criterion for the Steinberg algebra A(S)(G(E)) of the graph groupoid G(E) associated to an arbitrary graph E to be congruence-simple. Motivated by a result of Clark and Sims, we show that the natural homomorphism from the Leavitt path algebra L-B(E) to the Steinberg algebra A(B)(G(E)), where B is the Boolean semifield, is an isomorphism if and only if E is row-finite. Moreover, we establish the Reduction Theorem and Uniqueness Theorems for Leavitt path algebras of row-finite graphs over the Boolean semifield B. (C) 2020 Elsevier B.V. All rights reserved. (AU) | |
| FAPESP's process: | 18/06538-6 - Leavitt path algebras, Steinberg algebras and partial actions |
| Grantee: | Tran Giang Nam |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |