Crossed modules for Hom-Lie–Rinehart algebras
Volume 152 / 2018
Colloquium Mathematicum 152 (2018), 1-14
MSC: Primary 17B99; Secondary 18D35.
DOI: 10.4064/cm7170-3-2017
Published online: 12 January 2018
Abstract
We introduce the notion of crossed modules for Hom-Lie–Rinehart algebras. A detailed study of their construction from actions and semidirect products of Hom-Lie–Rinehart algebras is given. We also introduce the notions of cat${^1}$-Hom-Lie–Rinehart algebras. It is proved that the category of crossed modules of Hom-Lie–Rinehart algebras and the category of cat${^1}$-Hom-Lie–Rinehart algebras are equivalent to each other.
