Emre ÖZEL, Ummahan EGE ARSLAN

On Quasi Quadratic Modules of Lie Algebras

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,

PDF

___

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.