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arXiv · 1602.02424

Twisted partial actions and extensions of semilattices of groups by groups

Mikhailo Dokuchaev·Mykola Khrypchenko
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Abstract

We introduce the concept of an extension of a semilattice of groups $A$ by a group $G$ and describe all the extensions of this type which are equivalent to the crossed products $A*_\Theta G$ by twisted partial actions $\Theta$ of $G$ on $A$. As a consequence, we establish a one-to-one correspondence, up to an isomorphism, between twisted partial actions of groups on semilattices of groups and so-called Sieben twisted modules over $E$-unitary inverse semigroups.

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Mikhailo Dokuchaev, Mykola Khrypchenko. 2016-02-07. Twisted partial actions and extensions of semilattices of groups by groups. https://arxiv.org/abs/1602.02424

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