Hecke-Kiselman monoid的生长替代方案

Pub Date : 2019-01-01 DOI:10.5565/PUBLMAT6311907

Arkadiusz Mȩcel, J. Okniński

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引用次数: 8

摘要

研究了有向图定义的Hecke-Kiselman代数的Gelfand-Kirillov维数。证明了当且仅当底层图包含由一条(有向)路径连接的两个环时，维数是无限的。而且，在这种情况下，Hecke-Kiselman单群包含一个自由非交换子单群。当且仅当一元代数满足多项式恒等式时，维数是有限的。2010数学学科分类:16P90、16S15、16S36、16S99、20M05。

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Growth alternative for Hecke-Kiselman monoids

The Gelfand–Kirillov dimension of Hecke–Kiselman algebras defined by oriented graphs is studied. It is shown that the dimension is infinite if and only if the underlying graph contains two cycles connected by an (oriented) path. Moreover, in this case, the Hecke–Kiselman monoid contains a free noncommutative submonoid. The dimension is finite if and only if the monoid algebra satisfies a polynomial identity. 2010 Mathematics Subject Classification: 16P90, 16S15, 16S36, 16S99, 20M05.

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