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-a...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.展开更多
文摘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.
