• https://mat.upc.edu/ca/activitats/conferencia-leavitt-path-algebra
• Conferència Leavitt path algebra
• 2022-11-04T12:00:00+01:00
• 2022-11-04T17:00:00+01:00
• Talented Monoid Graded Classification Conjecture: an Evidence and a Finite-case Confirmation. Presented by Alfilgen N. Sebandal, Mindanao State University-Iligan Institute of Technology (MSU-IIT), Philippines.

Talented Monoid Graded Classification Conjecture: an Evidence and a Finite-case Confirmation. Presented by Alfilgen N. Sebandal, Mindanao State University-Iligan Institute of Technology (MSU-IIT), Philippines.

Quan

04/11/2022 de 12:00 a 17:00

On

Aula 22 de la Facultat de Nàutica

Nom de contacte

Alfilgen N. Sebandal

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Given a directed graph, one can associate two algebraic entities: the Leavitt path algebra and the talented monoid which has interesting relationship between them.

The talented monoid is isomorphic to the positive cone of the graded K0-group of the Leavitt path algebra which is naturally equipped with a Z-action. In this talk, we characterise directed graphs consisting of disjoint cycles via their talented monoids by introducing types of Z-order-ideals. We show that a graph E consists of disjoint cycles precisely when its talented monoid TE has a particular Jordan-Hölder composition series. These are graphs whose associated Leavitt path algebras have finite Gelfand-Kirillov dimension. We show that this dimension can be determined as the length of suitable ideal series of the talented monoid.

The last part of the talk is a brief overview of the talented monoid as an invariant for finite representation of Leavitt path algebras. This is a confirmation of the Graded Classification Conjecture of the Leavitt path algebras in the finite-dimensional case.