Homology, Homotopy and Applications

Volume 22 (2020)

Number 2

Crossed modules in the category of Loday QD-Rinehart algebras

Pages: 347 – 366

DOI: https://dx.doi.org/10.4310/HHA.2020.v22.n2.a21


J. M. Casas (Department of Applied Mathematics, University of Vigo, Pontevedra, Spain)

S. Çetin (Department of Mathematics, Faculty of Arts and Sciences, Burdur Mehmet Akif Ersoy University, Burdur, Turkey)

E. Ö. Uslu (Department of Applied Mathematics, University of Vigo, Pontevedra, Spain)


In this paper we introduce the notion of Loday QD-Rinehart algebra as an abstraction of Loday QD-algebroids. Additionally, we study cohomology groups, derivations, abelian extensions and crossed modules of these algebraic structures and analyze the relationships between them.


Loday QD-algebroid, Loday QD-Rinehart algebra, derivation, abelian extension, crossed module, cohomology

2010 Mathematics Subject Classification

17A32, 17D99, 18G60

The first author was supported by Agencia Estatal de Investigación (Spain), grant MTM2016-79661-P (AEI/FEDER, UE, support included).

Received 31 January 2019

Received revised 5 November 2019

Accepted 5 February 2020

Published 20 May 2020