Undecidability of the word problem for one-relator inverse monoids

Abstract: It is a classical result of Magnus proved in the 1930s that the word problem is decidable for one-relator groups. This result inspired a series of investigations of the word problem in other one-relator algebraic structures. For example, in the 1960s Shirshov proved the word problem is decidable in one-relator Lie algebras. In contrast, it remains a longstanding open problem whether the word problem is decidable for one-relator monoids. An important class of algebraic structures lying in between monoids and groups is that of inverse monoids. In this talk I will speak about a recent result which shows that there exist one-relator inverse monoids of the form Inv with undecidable word problem. This answers a problem originally posed by Margolis, Meakin and Stephen in 1987. I will explain how this result relates to the word problem for one-relator monoids, the submonoid membership problem for one-relator groups, and to the question of which right-angled Artin groups arise as subgroups of one-relator groups.

operator algebrasrings and algebras

Audience: researchers in the topic

Western Sydney University Abend Seminars

Series comments: Description: Western Sydney University Abend Seminars

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