Leavitt path algebras, Steinberg algebras and partial actions

• Grant number: 18/06538-6
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: January 01, 2019
• Status: Discontinued
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Mikhailo Dokuchaev
• Grantee: Tran Giang Nam
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 15/09162-9 - Non commutative algebra and applications, AP.TEM

Abstract

The ``prehistorical'' beginning of Leavitt path algebras started with Leavitt algebras, Bergman algebras, and graph C*-algebras, considering rings with the Invariant Basis Number property, universal ring constructions, and the structure of separable simple infinite C*-algebras. During the past decade, Leavitt path algebras become a subject of intense investigation by researchers from different areas of mathematics. Recently, Leavitt path algebars as well as Steinberg algebras were interpreted as crossed product by partial actions, establishing a possibility of an interplay between these areas. Our main goals are as follows: - Find graph-theoretic conditions on rhe graph which describe precisely the Leavitt path algebras having the Invariant Basis Number proper- Find relations between two graphs such that their associated Leavitt path algebras are Morita equivalent.- Calculate the global dimension of the Steinberg algebra of an ample groupoid.- Consider skew group rings by partial actions in interaction with the theories of Leavitt path and Steinberg algebras.

Scientific publications

(4)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

ABRAMS, G.; DOKUCHAEV, M.; NAM, T. G.. Realizing corners of Leavitt path algebras as Steinberg algebras, with corresponding connections to graph C{*}-algebras. Journal of Algebra, v. 593, p. 72-104, MAR 1 2022. (20/16594-0, 18/06538-6)

TRAN GIANG NAM; ZUMBRAEGEL, JENS. On Steinberg algebras of Hausdorff ample groupoids over commutative semirings. Journal of Pure and Applied Algebra, v. 225, n. 4, p. 22-pg., 2021-04-01. (18/06538-6)

ANH, P. N.; NAM, T. G.. Special irreducible representations of Leavitt path algebras. ADVANCES IN MATHEMATICS, v. 377, JAN 22 2021. (18/06538-6)

ABRAMS, GENE; NAM, TRAN GIANG. Corners of Leavitt path algebras of finite graphs are Leavitt path algebras. Journal of Algebra, v. 547, p. 494-518, APR 1 2020. (18/06538-6)