On Quasi Quadratic Modules of Lie Algebras

Year 2022, Issue: 41, 62 - 69, 31.12.2022

Emre Özel , Ummahan Ege Arslan

https://doi.org/10.53570/jnt.1176779

Cited By: 3

https://izlik.org/JA66EP53XP

Abstract

This study introduces the category of quasi-quadratic modules of Lie algebras and discusses the functorial relations between quasi-quadratic modules and quadratic modules of Lie algebras.

Keywords

Crossed modules , quasi quadratic modules , quadratic modules

References

• J. H. C. Whitehead, Combinatorial homotopy I, Bulletin of the American Mathematical Society 55 (3) (1949) 213–245.
• J. H. C. Whitehead, Combinatorial homotopy II, Bulletin of the American Mathematical Society 55 (5) (1949) 453–496.
• C. Kassel, J. L. Loday, Extensions Centrales D’algébres de Lie, Annales de l’institut Fourier 33 (1982) 119–142.
• D. Conduch_e, Modules Crois_es Généralisés de Longueur 2, Journal of Pure and Applied Algebra 34 (1984) 155–178.
• G. J. Ellis, Homotopical Aspects of Lie Algebras, Journal of the Australian Mathematical Society (Series A) 54 (1993) 393–419.
• H. J. Baues, Combinatorial Homotopy and 4-Dimensional Complexes, De Gruyter, Berlin, 1991.
• E. Ulualan, E. Uslu, Quadratic Modules for Lie Algebras, Hacettepe Journal of Mathematics and Statistics 40 (3) (2011) 409–419.
• Z. Arvasi, E. Ulualan, Quadratic and 2-Crossed Modules of Algebras, Algebra Colloquium 14 (4) (2007) 669–686.
• Z. Arvasi, E. Ulualan, On Algebraic Models for Homotopy 3-Types, Journal of Homotopy and Related Structures 1 (1) (2006) 1–27.
• E. Soylu Yılmaz, K. Yılmaz, On Relations Among Quadratic Modules, Mathematical Methods in the Applied Sciences 1 (1) (2022) 1–13.
• U. Ege Arslan, E. Özel, On Homotopy Theory of Quadratic Modules of Lie Algebras, Konuralp Journal of Mathematics 10 (1) (2022) 159–165.
• E. Özel, Lie Pointed Homotopy Theory of Quadratic Modules of Lie Algebras, Master’s Thesis, Eskişehir Osmangazi University (2017) Eskişehir, Türkiye.
• İ. İ. Akça, K. Emir, J. F. Martins, Pointed Homotopy of Between 2-Crossed Modules of Commutative Algebras, Homology, Homotopy and Applications 17 (2) (2015) 1–30.
• B. Gohla, J. Faria Martins, Pointed Homotopy and Pointed Lax Homotopy of 2-Crossed Module Maps, Advances in Mathematics 248 (2013) 986–1049.
• P. Carrasco, T. Porter, Coproduct of 2-Crossed Modules: Applications to a Definition of a Tensor Product for 2-Crossed Complexes, Collectanea Mathematica 67 (2016) 485–517.
• U. Ege Arslan, S. Kaplan, On Quasi 2-Crossed Modules for Lie Algebras and Functorial Relations, Ikonion Journal of Mathematics 4 (1) (2022) 17–26.