Affiliation:
1. Institute of Mathematics , University of Warsaw , Banacha 2, 02-097 Warsaw , Poland
Abstract
Abstract
Hecke–Kiselman algebras
A
Θ
{A_{\Theta}}
, over a field
𝕂
{\mathbb{K}}
, associated to finite
oriented graphs Θ are considered. It has been known that every such algebra
is an automaton algebra in the sense of Ufranovskii. In particular, its
Gelfand–Kirillov dimension is an integer if it is finite.
In this paper, a numerical invariant of the graph Θ that determines
the dimension of
A
Θ
{A_{\Theta}}
is found.
Namely, we prove that the Gelfand–Kirillov dimension of
A
Θ
{A_{\Theta}}
is the
sum of the number of cyclic subgraphs of Θ and the number of oriented paths
of a special type in the graph, each counted certain specific number of times.
Subject
Applied Mathematics,General Mathematics
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