Research Article
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On Quasi Quadratic Modules of Lie Algebras

Year 2022, Issue: 41, 62 - 69, 31.12.2022
https://doi.org/10.53570/jnt.1176779

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

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

Emre Özel 0000-0002-5106-443X

Ummahan Ege Arslan 0000-0002-2995-0718

Publication Date December 31, 2022
Submission Date September 17, 2022
Published in Issue Year 2022 Issue: 41

Cite

APA Özel, E., & Ege Arslan, U. (2022). On Quasi Quadratic Modules of Lie Algebras. Journal of New Theory(41), 62-69. https://doi.org/10.53570/jnt.1176779
AMA Özel E, Ege Arslan U. On Quasi Quadratic Modules of Lie Algebras. JNT. December 2022;(41):62-69. doi:10.53570/jnt.1176779
Chicago Özel, Emre, and Ummahan Ege Arslan. “On Quasi Quadratic Modules of Lie Algebras”. Journal of New Theory, no. 41 (December 2022): 62-69. https://doi.org/10.53570/jnt.1176779.
EndNote Özel E, Ege Arslan U (December 1, 2022) On Quasi Quadratic Modules of Lie Algebras. Journal of New Theory 41 62–69.
IEEE E. Özel and U. Ege Arslan, “On Quasi Quadratic Modules of Lie Algebras”, JNT, no. 41, pp. 62–69, December 2022, doi: 10.53570/jnt.1176779.
ISNAD Özel, Emre - Ege Arslan, Ummahan. “On Quasi Quadratic Modules of Lie Algebras”. Journal of New Theory 41 (December 2022), 62-69. https://doi.org/10.53570/jnt.1176779.
JAMA Özel E, Ege Arslan U. On Quasi Quadratic Modules of Lie Algebras. JNT. 2022;:62–69.
MLA Özel, Emre and Ummahan Ege Arslan. “On Quasi Quadratic Modules of Lie Algebras”. Journal of New Theory, no. 41, 2022, pp. 62-69, doi:10.53570/jnt.1176779.
Vancouver Özel E, Ege Arslan U. On Quasi Quadratic Modules of Lie Algebras. JNT. 2022(41):62-9.


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