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Mock-Lie bialgebras and mock-Lie analogue of the classical Yang-Baxter equation
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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 O-operators are studied to construct skew-symmetric solution of mock-Lie Yang-Baxter equation.
M. S. C (2020):16W10, 16T10, 16T15, 16T25, 17B38.
Title: Mock-Lie bialgebras and mock-Lie analogue of the classical Yang-Baxter equation
Description:
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 O-operators are studied to construct skew-symmetric solution of mock-Lie Yang-Baxter equation.
M.
S.
C (2020):16W10, 16T10, 16T15, 16T25, 17B38.
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