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On Homotopy Theory of Quadratic Modules of Lie Algebras

Year 2022, Volume: 10 Issue: 1, 159 - 165, 15.04.2022

Ummahan Ege Arslan Emre Özel

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

Quadratic modules crossed modules homotopy.

Supporting Institution

Eskisehir Osmangazi University, Scientific Research Center (BAP)

Project Number

2017-1574

References

  • [1] ˙I. Akc¸a and Z. Arvasi, Simplicial and crossed Lie algebras, Homology, Homotopy and Applications 4 (1), 43–57, 2002.
  • [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] ˙I. Akc¸a and Yavuz Sıdal, Homotopies of Lie Crossed module morphisms,Konuralp Journal of Mathematics, 6,2, 259-263, 2018.
  • [4] H. J. Baues, Combinatorial homotopy and 4-dimensional complexes,Berlin,etc.: Walter de Gruyter, 1991.
  • [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] D. Conduch´e, Modules crois´es g´en´eralis´es de longueur 2, J. Pure Appl. Algebra, 34:155–178,1984.
  • [7] G. J. Ellis, Homotopical aspects of Lie algebras, J. Austral. Math. Soc. (Series A) 54, 393–419, 1993.
  • [8] J. Faria Martins, The fundamental 2-crossed complex of a reduced CW-complex, Homology Homotopy Appl., 13(2):129–157, 2011.
  • [9] B. Gohla and J. Faria Martins, Pointed homotopy and pointed lax homotopy of 2-crossed module maps, Adv. Math., 248:986–1049, 2013.
  • [10] C. Kassel and J.L. Loday, Extensions centrales d’alg´ebres de Lie, Ann. Inst. Fourier (Grenoble) 33, 119–142, 1982.
  • [11] E. O¨ zel, Lie cebirlerin kuadratik modu¨llerinin noktasal homotopi teorisi , M. Sc. Thesis, Eskis¸ehir Osmangazi University,FBE, 2017.
  • [12] E. Ulualan, and E. Uslu, Quadratic Modules for Lie Algebras, Hacettepe Journal of Mathematics and Statistics, 40,3, pp. 409–419, 2011.
  • [13] K.Yılmaz and E.Soylu Yılmaz, Baues cofibration for quadratic modules of Lie algebras, Communications Faculty of Sciences University of Ankara Series A1 Math. and Statistics,68,2, 1653 - 1663, 2019,
  • [14] K.Yılmaz and E.Soylu Yılmaz, A. G¨uzelkokar, XModLie Fibred Over Lie Algebras, Ikonion Journal of Mathematics,3,2,9 - 16,2021.

Year 2022, Volume: 10 Issue: 1, 159 - 165, 15.04.2022

Ummahan Ege Arslan Emre Özel

Abstract

Project Number

2017-1574

References

  • [1] ˙I. Akc¸a and Z. Arvasi, Simplicial and crossed Lie algebras, Homology, Homotopy and Applications 4 (1), 43–57, 2002.
  • [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] ˙I. Akc¸a and Yavuz Sıdal, Homotopies of Lie Crossed module morphisms,Konuralp Journal of Mathematics, 6,2, 259-263, 2018.
  • [4] H. J. Baues, Combinatorial homotopy and 4-dimensional complexes,Berlin,etc.: Walter de Gruyter, 1991.
  • [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] D. Conduch´e, Modules crois´es g´en´eralis´es de longueur 2, J. Pure Appl. Algebra, 34:155–178,1984.
  • [7] G. J. Ellis, Homotopical aspects of Lie algebras, J. Austral. Math. Soc. (Series A) 54, 393–419, 1993.
  • [8] J. Faria Martins, The fundamental 2-crossed complex of a reduced CW-complex, Homology Homotopy Appl., 13(2):129–157, 2011.
  • [9] B. Gohla and J. Faria Martins, Pointed homotopy and pointed lax homotopy of 2-crossed module maps, Adv. Math., 248:986–1049, 2013.
  • [10] C. Kassel and J.L. Loday, Extensions centrales d’alg´ebres de Lie, Ann. Inst. Fourier (Grenoble) 33, 119–142, 1982.
  • [11] E. O¨ zel, Lie cebirlerin kuadratik modu¨llerinin noktasal homotopi teorisi , M. Sc. Thesis, Eskis¸ehir Osmangazi University,FBE, 2017.
  • [12] E. Ulualan, and E. Uslu, Quadratic Modules for Lie Algebras, Hacettepe Journal of Mathematics and Statistics, 40,3, pp. 409–419, 2011.
  • [13] K.Yılmaz and E.Soylu Yılmaz, Baues cofibration for quadratic modules of Lie algebras, Communications Faculty of Sciences University of Ankara Series A1 Math. and Statistics,68,2, 1653 - 1663, 2019,
  • [14] K.Yılmaz and E.Soylu Yılmaz, A. G¨uzelkokar, XModLie Fibred Over Lie Algebras, Ikonion Journal of Mathematics,3,2,9 - 16,2021.
There are 14 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Ummahan Ege Arslan

Emre Özel 0000-0003-1883-5172

Project Number 2017-1574
Publication Date April 15, 2022
Submission Date March 7, 2022
Acceptance Date March 22, 2022
Published in Issue Year 2022 Volume: 10 Issue: 1

Cite

APA Ege Arslan, U., & Özel, E. (2022). On Homotopy Theory of Quadratic Modules of Lie Algebras. Konuralp Journal of Mathematics, 10(1), 159-165.
AMA Ege Arslan U, Özel E. On Homotopy Theory of Quadratic Modules of Lie Algebras. Konuralp J. Math. April 2022;10(1):159-165.
Chicago Ege Arslan, Ummahan, and Emre Özel. “On Homotopy Theory of Quadratic Modules of Lie Algebras”. Konuralp Journal of Mathematics 10, no. 1 (April 2022): 159-65.
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 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, 2022.
ISNAD Ege Arslan, Ummahan - Özel, Emre. “On Homotopy Theory of Quadratic Modules of Lie Algebras”. Konuralp Journal of Mathematics 10/1 (April 2022), 159-165.
JAMA 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, 2022, pp. 159-65.
Vancouver Ege Arslan U, Özel E. On Homotopy Theory of Quadratic Modules of Lie Algebras. Konuralp J. Math. 2022;10(1):159-65.
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