- Hacettepe Journal of Mathematics and Statistics
- Vol: 51 Issue: 1
- Deformation of Kupershmidt operators and Kupershmidt-Nijenhuis structures of a Malcev algebra
Deformation of Kupershmidt operators and Kupershmidt-Nijenhuis structures of a Malcev algebra
Authors : Sami Mabrouk
Pages : 199-217
Doi:10.15672/hujms.923905
View : 12 | Download : 3
Publication Date : 2022-02-14
Article Type : Research
Abstract :The aim of this paper is to study infinitesimal deformations of a Malcev algebra with a representation and introduce the notion of Nijenhuis pair, which gives a trivial deformation of a Malcev algebra with a representation. We introduce the notion of Kupershmidt-(dual-)Nijenhuis structure on a Malcev algebra with a representation. Furthermore, we show that a Kupershmidt-(dual-)Nijenhuis structure gives rise to a hierarchy of Kupershmidt operators. Finally, we establish a deformation theory of Kupershmidt operators in consistence with the general principles of deformation theories and introduce the notion of Nijenhuis elements.Keywords : altenative algebras, Malcev algebras, representations, (dual-)Nijenhuispair, Kupershmidt operator, Kupershmidt-(dual-)Nijenhuis structure