Hom-L-dendriform代数与Hom-L-quadri代数

Hom-L-dendriform代数和Hom-L-quadri代数分别是由L-dendriform代数和L-quadri代数通过代数形变得出的。引入Hom-L-dendriform代数和Hom-L-quadri代数的定义,给出了利用L-dendriform代数以及L-dendriform代数上的代数同态构造Hom-L-dendriform代数的方法,同时给出利用Lquadri代数以及L-quadri代数上的代数同态构造Hom-L-quadri代数的方法,最后给出Hom-pre-Lie代数、Hom-L-dendriform代数和Hom-L-quadri代数之间的关系。

L-octo-algebras

L-octo-algebra with 8 operations as the Lie algebraic analogue of octo- algebra such that the sum of 8 operations is a Lie algebra is discussed. Any octo- algebra is an L-octo-algebra. The relationships among L-octo-algebras, L-quadri- algebras, L-dendriform algebras, pre-Lie algebras and Lie algebras are given. The close relationships between L-octo-algebras and some interesting structures like Rota- Baxter operators, classical Yang-Baxter equations and some bilinear forms satisfying certain conditions are given also.