On Quasi 2-Crossed Modules for Lie Algebras and Functorial Relations

Year 2022, Volume: 4 Issue: 1, 17 - 26, 23.09.2022

Ummahan Ege Arslan , Sultan Kaplan

https://doi.org/10.54286/ikjm.1089611

Cited By: 2

Abstract

In this paper, we have introduced the category of 2-quasi crossed modules for Lie algebras and we have constructed a pair of adjoint functors between this category and that of 2-crossed modules Lie algebras.

Keywords

2-Quasi Crossed Modules of Lie Algebras, 2-Crossed Modules of Lie Algebras, adjunction

Supporting Institution

Eskisehir Osmangazi University, Scientific Research Center (BAP)

Project Number

202019A107

References

• D. Conduch'e, Modules crois'es g'en'eralis'es de longueur 2, J. Pure Appl. Algebra, 34:155–178,1984.
• P.Carrasco, T. Porter, Coproduct of 2-crossed modules:applications to a definition of a tensor product for 2-crossed complexes, Collect. Math. DOI 10.1007/s13348-015-0156-9.
• G. J. Ellis, Homotopical aspects of Lie algebras}, J. Austral. Math. Soc. (Series A) 54, 393–419, 1993.
• C. Kassel and J.L. Loday, Extensions centrales d'alg\'ebres de Lie, Ann. Inst. Fourier (Grenoble) 33, 119–142, 1982.
• J.H.C Whitehead, Combinatorial homotopy II, Bulletin of the American Mathematical Society, vol. 55, pp. 453--496, 1949.