Pre-anti-flexible bialgebras

Dassoundo, Mafoya Landry

doi:10.1080/00927872.2021.1912065

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2023

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Cited by 3 publications

(2 citation statements)

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“…A good compatibility condition is prescribed on one hand by a strong motivation and potential applications, and on the other hand by a rich structure theory and effective constructions. See also [20,9,16,25,26,27,33,34,38,39,40,24,23] for more details.…”

Section: Introductionmentioning

confidence: 99%

Bialgebras, the Yang–Baxter equation and Manin triples for mock-Lie algebras

Chtioui,

Benali,

Hajjaji

et al. 2023

ACUTM

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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.

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Section: Introductionmentioning

confidence: 99%

Bialgebras, the Yang–Baxter equation and Manin triples for mock-Lie algebras

Chtioui,

Benali,

Hajjaji

et al. 2023

ACUTM

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show abstract

“…The theory of Manin triples and anti-flexible Yang-Baxter equation for anti-flexible algebras are developed in the same paper. Pre-anti-flexible algebras and pre-anti-flexible bialgebras are studied by Dassoundo in [12,13].…”

Section: Introductionmentioning

confidence: 99%