RT Conference Proceedings
T1 The Talented monoid of a graph and its connections with the Leavitt path algebra
A1 Sebandal, Alfilgen
K1 Álgebra
AB In this talk, we introduce an algebraic entity arising from a directed graph - the talented monoid.The talented monoid has an interesting relationship with the Leavitt path algebra. In fact, the groupcompletion of the talented monoid was shown to be the graded Grothendieck group of the Leavitt pathalgebra. We show that a graph consists of disjoint cycles precisely when its talented monoid has aparticular Jordan-Holder composition series. These are graphs whose associated Leavitt path algebrashave finite Gelfand-Kirillov dimension. We show that this dimension can be determined as the length ofsuitable ideal series of the talented monoid. The last part of the talk is a brief overview of the talentedmonoid as an invariant for finite representation of Leavitt path algebras. This is a confirmation of theGraded Classification Conjecture of the Leavitt path algebras in the finite-dimensional case.
YR 2022
FD 2022
LK https://hdl.handle.net/10630/25311
UL https://hdl.handle.net/10630/25311
LA eng
NO Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech.
DS RIUMA. Repositorio Institucional de la Universidad de Málaga
RD 20 ene 2026