Twisted partial actions and extensions of semilattices of groups by groups

Author(s)

Dokuchaev, Mikhailo ^[1] ; Khrypchenko, Mykola ^[2]

Affiliation

^[1] Univ Sao Paulo, Inst Matemat & Estat, Rua Matao 1010, BR-05508090 Sao Paulo, SP - Brazil

^[2] Univ Fed Santa Catarina, Dept Matemat, Campus Reitor Joao David Ferreira Lima, BR-88040900 Florianopolis, SC - Brazil

• Document type: Journal article
• Source: INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION; v. 27, n. 7, p. 887-933, NOV 2017.
• Web of Science Citations: 2

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. (AU)

• FAPESP's process: 12/01554-7 - Partial actions and representations, cohomology and globalization
• Grantee: Mykola Khrypchenko
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• FAPESP's process: 15/09162-9 - Non commutative algebra and applications
• Grantee: Francisco Cesar Polcino Milies
• Support Opportunities: Research Projects - Thematic Grants