Bialgebras, the Yang–Baxter equation and Manin triples for mock-Lie algebras
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Published:2023-12-01
Issue:2
Volume:27
Page:211-233
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ISSN:2228-4699
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Container-title:Acta et Commentationes Universitatis Tartuensis de Mathematica
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language:
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Short-container-title:ACUTM
Author:
Chtioui TaoufikORCID,
Benali KarimaORCID,
Hajjaji AtefORCID,
Mabrouk SamiORCID
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 introducing 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, O-operators are studied to construct a skew-symmetric solution of a mock-Lie Yang–Baxter equation.
Publisher
University of Tartu
Subject
General Mathematics