Cleft extensions for quasi-entwining structures

In this paper we introduce the notions of quasi-entwining structure and cleft extension for a quasi-entwining structure. We prove that if ( , , ) is a quasi-entwining structure and the associated extension to the submagma of coinvariants is cleft, there exists an isomorphism between ⊗ and . Moreover...

Full description

Saved in:
Bibliographic Details
Published inMathematica Slovaca Vol. 68; no. 2; pp. 339 - 352
Main Authors Alonso Álvarez, J. N., Fernández Vilaboa, J. M., González Rodríguez, R.
Format Journal Article
LanguageEnglish
Published Heidelberg De Gruyter 25.04.2018
Walter de Gruyter GmbH
Subjects
18D10
81R50
cleft extension
Hopf (co)quasigroup
Isomorphism
Magma
monoidal category
Primary 17A01
quasi-entwining structure
Secondary 16T05
Online AccessGet full text

Cover

More Information
Summary:In this paper we introduce the notions of quasi-entwining structure and cleft extension for a quasi-entwining structure. We prove that if ( , , ) is a quasi-entwining structure and the associated extension to the submagma of coinvariants is cleft, there exists an isomorphism between ⊗ and . Moreover, we define two unital but not necessarily associative products on ⊗ . For these structures we obtain the necessary and sufficient conditions to assure that is a magma isomorphism, giving some examples fulfilling these conditions.
ISSN:0139-9918
1337-2211
DOI:10.1515/ms-2017-0105