Frontiers of Mathematics in China >
Nijenhuis algebras, NS algebras, and N-dendriform algebras
Received date: 04 Feb 2012
Accepted date: 07 Jun 2012
Published date: 01 Oct 2012
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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 RotaBaxter 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.
Peng LEI , Li GUO . Nijenhuis algebras, NS algebras, and N-dendriform algebras[J]. Frontiers of Mathematics in China, 2012 , 7(5) : 827 -846 . DOI: 10.1007/s11464-012-0225-2
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