9 papers
Growth functions of algebras and an application to Leavitt path algebras
João Schwarz, Alfilgen Sebandal
In this paper, we consider three growth functions of algebras: the Gelfand-Kirillov dimension, superdimension, and entropy -- as well as a variation of the latter successfully used…
Properties of the -Monoid of Weighted Leavitt Path Algebras
Rishabh Goswami, Alfilgen Sebandal
For a row-finite weighted graph , Preusser showed that the monoid of finitely generated projective modules over the weighted Leavitt path algebra $L_…
Morita theory of finite representations of Leavitt path algebras
Wolfgang Bock, Roozbeh Hazrat, Alfilgen Sebandal
The Graded Classification Conjecture states that for finite directed graphs and , the associated Leavitt path algebras $L_\K(E)$ and $L_\K(F)$ are graded Morita equivalent,…
The algebraic entropies of the Leavitt path algebra and the graph algebras agree
Wolfgang Bock, Cristóbal Gil Canto, Dolores Martín Barquero +3
In this note we prove that the algebras and have the same entropy. Entropy is always referred to the standard filtrations in the corresponding kind of algebra. The ma…
Algebraic entropy and a complete classification of path algebras over finite graphs by growth
Wolfgang Bock, Cristóbal Gil Canto, Dolores Martín Barquero +3
The Gelfand-Kirillov dimension is a well established quantity to classify the growth of infinite dimensional algebras. In this article we introduce the algebraic entropy for path a…
An Adjacency Matrix Perspective of Talented Monoids and Leavitt Path Algebras
Wolfgang Bock, Alfilgen Sebandal
In this article we establish relationships between Leavitt path algebras, talented monoids and the adjacency matrices of the underlying graphs. We show that indeed the adjacency ma…
A Talented Monoid View on Lie Bracket Algebras over Leavitt Path Algebras
Wolfgang Bock, Alfilgen Sebandal, Jocelyn Viliela
In this article, we study properties as simplicity, solvability and nilpotency for Lie bracket algebras arising from Leavitt path algebras, based on the talented monoid of the unde…
The Jordan-Hölder Theorem for Monoids with Group Action
Alfilgen Sebandal, Jocelyn P. Vilela
In this article, we prove an isomorphism theorem for the case of refinement -monoids. Based on this we show a version of the well-known Jordan-Hölder theorem in this framework.…
Graphs with disjoint cycles, classification via the talented monoid
Roozbeh Hazrat, Alfilgen N. Sebandal, Jocelyn P. Vilela
We characterise directed graphs consisting of disjoint cycles via their talented monoids. We show that a graph consists of disjoint cycles precisely when its talented monoid $T…