NDLI: Nijenhuis algebras, NS algebras, and N-dendriform algebras

Content Provider	Springer Nature Link
Author	Lei, Peng Guo, Li
Copyright Year	2012
Abstract	In this paper, we study (associative) Nijenhuis algebras, with emphasis on the relationship between the category of Nijenhuis algebras and the categories of NS algebras and related algebras. This is in analogy to the well-known theory of the adjoint functor from the category of Lie algebras to that of associative algebras, and the more recent results on the adjoint functor from the categories of dendriform and tridendriform algebras to that of Rota-Baxter algebras. We first give an explicit construction of free Nijenhuis algebras and then apply it to obtain the universal enveloping Nijenhuis algebra of an NS algebra. We further apply the construction to determine the binary quadratic nonsymmetric algebra, called the N-dendriform algebra, that is compatible with the Nijenhuis algebra. As it turns out, the N-dendriform algebra has more relations than the NS algebra.
Starting Page	827
Ending Page	846
Page Count	20
File Format	PDF
ISSN	16733452
Journal	Frontiers of Mathematics in China
Volume Number	7
Issue Number	5
e-ISSN	16733576
Language	English
Publisher	SP Higher Education Press
Publisher Date	2012-08-22
Publisher Institution	Chinese Universities
Publisher Place	Heidelberg
Access Restriction	Subscribed
Subject Keyword	Nijenhuis algebras Rota-Baxter algebras dendriform algebras NS algebras N-dendriform algebras Mathematics
Content Type	Text
Resource Type	Article
Subject	Mathematics

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