对合导子构造的3-李双代数与3-Pre-李代数
3-Lie Bialgebras and 3-pre-Lie Algebras Induced by Involutive Derivations
研究具有对合导子的3-李代数的结构,证明了具有对合导子的m-维3-李代数A存在相容的3-Pre-李代数,且在2m-维半直积3-李代数Aad* A*上存在局部上循环3-李双代数结构.利用对合导子构造了3-李代数Aad* A*上的3-李Yang-Baxter方程的解和一类3-Pre-李代数,并构造了8-维和10-维局部上循环3-李双代数.
We studied the structure of 3-Lie algebras with involutive derivations, and proved that if A is an m-dimensional 3-Lie algebra with an involutive derivation, then there exists a compatible 3-pre-Lie algebra and a local cocycle 3-Lie bialgebraic structure on the 2m-dimensional semi-direct product 3-Lie algebra Aad* A*. By means of involutive derivations, we constructed the skew-symmetric solution of the 3-Lie classical Yang-Baxter equation in the 3-Lie algebra Aad* A*, a class of 3-pre-Lie algebras, and eight and ten dimensional local cocycle 3-Lie bialgebras.
3-李代数 / 对合导子 / 局部上循环3-李双代数 / 3-李Yang-Baxter方程 {{custom_keyword}} /
3-Lie algebra / Involutive derivation / Local cocycle 3-Lie bialgebra / 3-Lie classical Yang-Baxter equation {{custom_keyword}} /
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河北省自然科学基金项目(A2018201126)
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