HNN extensions of inverse semigroups and groupoids

N. D. Gilbert

doi:10.1016/j.jalgebra.2003.09.026

HNN extensions of inverse semigroups and groupoids

N. D. Gilbert

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

Abstract

We use the isomorphism between the categories of inverse semigroups and inductive groupoids to construct HNN extensions of inverse semigroups, where the associated inverse subsemigroups are order ideals of the base. Properties of groupoids then ensure that the base inverse semigroup always embeds in an HNN extension constructed in this way. Other properties of HNN extensions are determined, including a description of the maximal subgroups and of the maximal group image, and the structure of the inverse subsemigroup generated by the stable letters. Finally, some examples are given. © 2004 Elsevier Inc. All rights reserved.

Original language	English
Pages (from-to)	27-45
Number of pages	19
Journal	Journal of Algebra
Volume	272
Issue number	1
DOIs	https://doi.org/10.1016/j.jalgebra.2003.09.026
Publication status	Published - 1 Feb 2004

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10.1016/j.jalgebra.2003.09.026

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AB - We use the isomorphism between the categories of inverse semigroups and inductive groupoids to construct HNN extensions of inverse semigroups, where the associated inverse subsemigroups are order ideals of the base. Properties of groupoids then ensure that the base inverse semigroup always embeds in an HNN extension constructed in this way. Other properties of HNN extensions are determined, including a description of the maximal subgroups and of the maximal group image, and the structure of the inverse subsemigroup generated by the stable letters. Finally, some examples are given. © 2004 Elsevier Inc. All rights reserved.

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HNN extensions of inverse semigroups and groupoids

Abstract

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