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On Quasi 2-Crossed Modules for Lie Algebras and Functorial Relations

Year 2022, Volume: 4 Issue: 1, 17 - 26, 23.09.2022

Ummahan Ege Arslan Sultan Kaplan

https://doi.org/10.54286/ikjm.1089611
Cited By: 2

Abstract

In this paper, we have introduced the category of 2-quasi crossed modules for Lie algebras and we have constructed a pair of adjoint functors between this category and that of 2-crossed modules Lie algebras.

Keywords

2-Quasi Crossed Modules of Lie Algebras 2-Crossed Modules of Lie Algebras adjunction

Supporting Institution

Eskisehir Osmangazi University, Scientific Research Center (BAP)

Project Number

202019A107

References

  • D. Conduch'e, Modules crois'es g'en'eralis'es de longueur 2, J. Pure Appl. Algebra, 34:155–178,1984.
  • P.Carrasco, T. Porter, Coproduct of 2-crossed modules:applications to a definition of a tensor product for 2-crossed complexes, Collect. Math. DOI 10.1007/s13348-015-0156-9.
  • G. J. Ellis, Homotopical aspects of Lie algebras}, J. Austral. Math. Soc. (Series A) 54, 393–419, 1993.
  • C. Kassel and J.L. Loday, Extensions centrales d'alg\'ebres de Lie, Ann. Inst. Fourier (Grenoble) 33, 119–142, 1982.
  • J.H.C Whitehead, Combinatorial homotopy II, Bulletin of the American Mathematical Society, vol. 55, pp. 453--496, 1949.

Year 2022, Volume: 4 Issue: 1, 17 - 26, 23.09.2022

Ummahan Ege Arslan Sultan Kaplan

https://doi.org/10.54286/ikjm.1089611
Cited By: 2

Abstract

Project Number

202019A107

References

  • D. Conduch'e, Modules crois'es g'en'eralis'es de longueur 2, J. Pure Appl. Algebra, 34:155–178,1984.
  • P.Carrasco, T. Porter, Coproduct of 2-crossed modules:applications to a definition of a tensor product for 2-crossed complexes, Collect. Math. DOI 10.1007/s13348-015-0156-9.
  • G. J. Ellis, Homotopical aspects of Lie algebras}, J. Austral. Math. Soc. (Series A) 54, 393–419, 1993.
  • C. Kassel and J.L. Loday, Extensions centrales d'alg\'ebres de Lie, Ann. Inst. Fourier (Grenoble) 33, 119–142, 1982.
  • J.H.C Whitehead, Combinatorial homotopy II, Bulletin of the American Mathematical Society, vol. 55, pp. 453--496, 1949.
There are 5 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Ummahan Ege Arslan

Sultan Kaplan 0000-0001-9520-8338

Project Number 202019A107
Early Pub Date March 10, 2022
Publication Date September 23, 2022
Acceptance Date May 11, 2022
Published in Issue Year 2022 Volume: 4 Issue: 1

Cite

APA Ege Arslan, U., & Kaplan, S. (2022). On Quasi 2-Crossed Modules for Lie Algebras and Functorial Relations. Ikonion Journal of Mathematics, 4(1), 17-26. https://doi.org/10.54286/ikjm.1089611
AMA Ege Arslan U, Kaplan S. On Quasi 2-Crossed Modules for Lie Algebras and Functorial Relations. ikjm. September 2022;4(1):17-26. doi:10.54286/ikjm.1089611
Chicago Ege Arslan, Ummahan, and Sultan Kaplan. “On Quasi 2-Crossed Modules for Lie Algebras and Functorial Relations”. Ikonion Journal of Mathematics 4, no. 1 (September 2022): 17-26. https://doi.org/10.54286/ikjm.1089611.
EndNote Ege Arslan U, Kaplan S (September 1, 2022) On Quasi 2-Crossed Modules for Lie Algebras and Functorial Relations. Ikonion Journal of Mathematics 4 1 17–26.
IEEE U. Ege Arslan and S. Kaplan, “On Quasi 2-Crossed Modules for Lie Algebras and Functorial Relations”, ikjm, vol. 4, no. 1, pp. 17–26, 2022, doi: 10.54286/ikjm.1089611.
ISNAD Ege Arslan, Ummahan - Kaplan, Sultan. “On Quasi 2-Crossed Modules for Lie Algebras and Functorial Relations”. Ikonion Journal of Mathematics 4/1 (September 2022), 17-26. https://doi.org/10.54286/ikjm.1089611.
JAMA Ege Arslan U, Kaplan S. On Quasi 2-Crossed Modules for Lie Algebras and Functorial Relations. ikjm. 2022;4:17–26.
MLA Ege Arslan, Ummahan and Sultan Kaplan. “On Quasi 2-Crossed Modules for Lie Algebras and Functorial Relations”. Ikonion Journal of Mathematics, vol. 4, no. 1, 2022, pp. 17-26, doi:10.54286/ikjm.1089611.
Vancouver Ege Arslan U, Kaplan S. On Quasi 2-Crossed Modules for Lie Algebras and Functorial Relations. ikjm. 2022;4(1):17-26.

Cited By

On Quasi Quadratic Modules of Lie Algebras
Journal of New Theory
https://doi.org/10.53570/jnt.1176779
4-Dimensional 2-Crossed Modules
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https://doi.org/10.53570/jnt.1148482
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