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arXiv · 2301.12928

Mock-Lie bialgebras and mock-Lie analogue of the classical Yang-Baxter equation

K. Benali·T. Chtioui·A. Hajjaji·S. Mabrouk
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Abstract

The aim of this paper is to introduce the notion of a mock-Lie bialgebra which is equivalent to a Manin triple of mock-Lie algebras. The study of a special case called coboundary mock-Lie bialgebra leads to the introduction the mock-Lie Yang-Baxter equation on a mock-Lie algebra which is an analogue of the classical Yang-Baxter equation on a Lie algebra. Note that a skew-symmetric solution of mock-Lie Yang-Baxter equation gives a mock-Lie bialgebra. Finally, the notation of $\mathcal O$-operators are studied to construct skew-symmetric solution of mock-Lie Yang-Baxter equation.

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BibTeXRIS

K. Benali, T. Chtioui, A. Hajjaji, S. Mabrouk. 2022-12-27. Mock-Lie bialgebras and mock-Lie analogue of the classical Yang-Baxter equation. https://arxiv.org/abs/2301.12928

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