Research Article
Year 2022,
Issue: 41, 62 - 69, 31.12.2022
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.
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.
Year 2022,
Issue: 41, 62 - 69, 31.12.2022
Abstract
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.
There are 16 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Research Article |
| Authors | |
| Publication Date | December 31, 2022 |
| Submission Date | September 17, 2022 |
| Published in Issue | Year 2022 Issue: 41 |
Cite
Cited By
Finite coproducts in the category of quadratic modules of Lie algebras
Journal of New Results in Science
https://doi.org/10.54187/jnrs.1184962
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