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- Title
Kupershmidt-(dual-)Nijenhuis structure on the alternative algebra with a representation.
- Authors
Sun, Qinxiu
- Abstract
The aim of this paper is to study Kupershmidt-(dual-)Nijenhuis structures on alternative algebras with representations. The notion of a (dual-)Nijenhuis pair is introduced and it can generate a trivial deformation of an alternative algebra with a representation. We introduce the notion of a Kupershmidt-(dual-)Nijenhuis structure on an alternative algebra with a representation. Furthermore, we verify that Kupershmidt operators and Kupershmidt-(dual-)Nijenhuis structures can give rise to each other under some conditions. Finally, we study the notions of Rota–Baxter–Nijenhuis structures and alternative r -matrix-Nijenhuis structures. Meanwhile, we investigate the relation between them.
- Subjects
REPRESENTATIONS of algebras
- Publication
Journal of Algebra & Its Applications, 2021, Vol 20, Issue 6, pN.PAG
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498821500973