대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제39권1호
  • /
  • Pages.11-30
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  • 2024
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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3-HOM-LIE SUPERBIALGEBRAS AND 3-HOM-LIE CLASSICAL YANG-BAXTER EQUATIONS

  • Issam Bartouli (Laboratoire de Mathematiques et Modelisation d'Evry (UMR 8071) Universite d'Evry Val d'Essonne) ;
  • Imed Basdouri (Faculty of Sciences Gafsa University of Gafsa) ;
  • Gaith Chaabane (Faculty of Sciences Sfax University of Sfax) ;
  • Mohamed Fadous (Faculty of Sciences Sfax University of Sfax) ;
  • Jean Lerbet (Laboratoire de Mathematiques et Modelisation d'Evry (UMR 8071) Universite d'Evry Val d'Essonne)
  • 투고 : 2023.03.13
  • 심사 : 2023.11.03
  • 발행 : 2024.01.31
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초록

3-Lie algebras are in close relationships with many fields. In this paper we are concerned with the study of 3-Hom-Lie super algebras, the concepts of 3-Hom-Lie coalgebras and how they make a 3-Hom-Lie superbialgebras, we study the structures of such categories of algebras and the relationships between each others. We study a super twisted 3-ary version of the Yang-Baxter equation, called the super 3-Lie classical Hom-Yang-Baxter equation (3-Lie CHYBE), which is a general form of 3-Lie classical Yang-Baxter equation and prove that the superbialgebras induced by the solutions of the super 3-Lie CHYBE induce the coboundary local cocycle 3-Hom-Lie superbialgebras.

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참고문헌

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