Research Article

On Homotopy Theory of Quadratic Modules of Lie Algebras

Volume: 10 Number: 1 April 15, 2022
EN

On Homotopy Theory of Quadratic Modules of Lie Algebras

Abstract

In this work, we will introduce the homotopy theory of quadratic modules over Lie algebras. We will construct a homotopy connecting one morphism of quadratic modules of Lie algebras to another.

Keywords

Supporting Institution

Eskisehir Osmangazi University, Scientific Research Center (BAP)

Project Number

2017-1574

References

  1. [1] ˙I. Akc¸a and Z. Arvasi, Simplicial and crossed Lie algebras, Homology, Homotopy and Applications 4 (1), 43–57, 2002.
  2. [2] ˙I. Akc¸a, K. Emir, and J. Faria Martins. Pointed homotopy of 2-crossed module maps on commutative algebras, Homology Homotopy Appl., 18(1):99–128, 2016.
  3. [3] ˙I. Akc¸a and Yavuz Sıdal, Homotopies of Lie Crossed module morphisms,Konuralp Journal of Mathematics, 6,2, 259-263, 2018.
  4. [4] H. J. Baues, Combinatorial homotopy and 4-dimensional complexes,Berlin,etc.: Walter de Gruyter, 1991.
  5. [5] R. Brown, P.J. Higgins, Tensor products and homotopies for w-groupoids and crossed complexes, J. Pure Appl. Algebra, 47 pp.1–33,1987.
  6. [6] D. Conduch´e, Modules crois´es g´en´eralis´es de longueur 2, J. Pure Appl. Algebra, 34:155–178,1984.
  7. [7] G. J. Ellis, Homotopical aspects of Lie algebras, J. Austral. Math. Soc. (Series A) 54, 393–419, 1993.
  8. [8] J. Faria Martins, The fundamental 2-crossed complex of a reduced CW-complex, Homology Homotopy Appl., 13(2):129–157, 2011.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Publication Date

April 15, 2022

Submission Date

March 7, 2022

Acceptance Date

March 22, 2022

Published in Issue

Year 2022 Volume: 10 Number: 1

APA
Ege Arslan, U., & Özel, E. (2022). On Homotopy Theory of Quadratic Modules of Lie Algebras. Konuralp Journal of Mathematics, 10(1), 159-165. https://izlik.org/JA46TP33ZD
AMA
1.Ege Arslan U, Özel E. On Homotopy Theory of Quadratic Modules of Lie Algebras. Konuralp J. Math. 2022;10(1):159-165. https://izlik.org/JA46TP33ZD
Chicago
Ege Arslan, Ummahan, and Emre Özel. 2022. “On Homotopy Theory of Quadratic Modules of Lie Algebras”. Konuralp Journal of Mathematics 10 (1): 159-65. https://izlik.org/JA46TP33ZD.
EndNote
Ege Arslan U, Özel E (April 1, 2022) On Homotopy Theory of Quadratic Modules of Lie Algebras. Konuralp Journal of Mathematics 10 1 159–165.
IEEE
[1]U. Ege Arslan and E. Özel, “On Homotopy Theory of Quadratic Modules of Lie Algebras”, Konuralp J. Math., vol. 10, no. 1, pp. 159–165, Apr. 2022, [Online]. Available: https://izlik.org/JA46TP33ZD
ISNAD
Ege Arslan, Ummahan - Özel, Emre. “On Homotopy Theory of Quadratic Modules of Lie Algebras”. Konuralp Journal of Mathematics 10/1 (April 1, 2022): 159-165. https://izlik.org/JA46TP33ZD.
JAMA
1.Ege Arslan U, Özel E. On Homotopy Theory of Quadratic Modules of Lie Algebras. Konuralp J. Math. 2022;10:159–165.
MLA
Ege Arslan, Ummahan, and Emre Özel. “On Homotopy Theory of Quadratic Modules of Lie Algebras”. Konuralp Journal of Mathematics, vol. 10, no. 1, Apr. 2022, pp. 159-65, https://izlik.org/JA46TP33ZD.
Vancouver
1.Ummahan Ege Arslan, Emre Özel. On Homotopy Theory of Quadratic Modules of Lie Algebras. Konuralp J. Math. [Internet]. 2022 Apr. 1;10(1):159-65. Available from: https://izlik.org/JA46TP33ZD
Creative Commons License
The published articles in KJM are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.