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

Authors : Sami MABROUK

Pages : 199-217

Doi:10.15672/hujms.923905

View : 15 | Download : 6

Publication Date : 2022-02-14

Article Type : Research Paper

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-insert ignore into journalissuearticles values(dual-);Nijenhuis structure on a Malcev algebra with a representation. Furthermore, we show that a Kupershmidt-insert ignore into journalissuearticles values(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