Volume 32, Issue 1
L-Octo-Algebras

Huihui An & Zhichun Wang

Commun. Math. Res., 32 (2016), pp. 57-69.

Published online: 2021-03

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  • Abstract

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.

  • Keywords

L-octo-algebra, L-quadri-algebra, bimodule.

  • AMS Subject Headings

17A30, 17B60

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-32-57, author = {An , Huihui and Wang , Zhichun}, title = {L-Octo-Algebras}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {32}, number = {1}, pages = {57--69}, abstract = {

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.

}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2016.01.04}, url = {http://global-sci.org/intro/article_detail/cmr/18662.html} }
TY - JOUR T1 - L-Octo-Algebras AU - An , Huihui AU - Wang , Zhichun JO - Communications in Mathematical Research VL - 1 SP - 57 EP - 69 PY - 2021 DA - 2021/03 SN - 32 DO - http://doi.org/10.13447/j.1674-5647.2016.01.04 UR - https://global-sci.org/intro/article_detail/cmr/18662.html KW - L-octo-algebra, L-quadri-algebra, bimodule. AB -

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.

Huihui An & Zhichun Wang. (2021). L-Octo-Algebras. Communications in Mathematical Research . 32 (1). 57-69. doi:10.13447/j.1674-5647.2016.01.04
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