Deformation of Kupershmidt operators and Kupershmidt-Nijenhuis structures of a Malcev algebra

Year 2022, Volume: 51 Issue: 1, 199 - 217, 14.02.2022

Sami Mabrouk

https://doi.org/10.15672/hujms.923905

Cited By: 3

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

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