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Year 2022, , 68 - 75, 31.07.2022

Hatice Taşbozan , Aydın Güzelkokar

https://doi.org/10.33773/jum.1089354

Abstract

References

  • [1] J.H.C. Whitehead, Combinatorial Homotopy II , Bull. Amer. Math. Soc. 55, 453496, 1949.
  • [2] D.M. Kan, A combinatorial definition of homotopy groups , Annals of Maths. 61, 288312, 1958.
  • [3] D. Conduch, Modules croiss gnraliss de longueur 2, J. Pure and Applied Algebra , 34,(1984), 155-178.
  • [4] G.J.Ellis,Homotopical aspects of Lie algebras, J. Austral. Math. Soc. (Series A),54, (1993), 393-419.
  • [5] A. Grothendieck, Catgories cobress additives et complexe cotangent relatif. In: Lecture Notes in Mathematics, vol. 79. Springer, Berlin (1968).
  • [6] D. Guin-Walery and J-L. Loday, Obsructiona l'excision en K-theorie algebrique, in: Algebraic K-Theory (Evanston 1980). Lecture Notes in Math. (1981), 179-216 (1981).
  • [7] H.J. Baues, Combinatorial homotopy and 4-dimensional complexes, Walter de Gruyter, 15, 1991.
  • [8] I. Aka and Z. Arvasi, Simplicial and crossed Lie algebras, Homology, Homotopy andApplications, Vol. 4 No.(1), (2002) ,43-57.
  • [9] Z. Arvasi and E. Ulualan, : Quadratic and 2-crossed modules of algebras. Algebra Colloquium. (14), 669-686 (2007).
  • [10] E.Ulualan and E.. Uslu, ,Quadratic modules for Lie algebras, Hacettepe Journal of Mathematics and Statistics, Vol40, (3), (2010), 409-419.
  • [11] H. Atik and E. Ulualan,Quadratic modules bibred over nil (2)-modules, Journal of Homotopy and Related Structures, 121, (2017), 83-108.
  • [12] K. Ylmaz,aprazlanm Kareler iin Bir Fibrasyon Uygulamas, Cumhuriyet Science Journal 391, (2018): 1-6.[13] K. Ylmaz and E.S. Ylmaz, Baues cobration for quadratic modules of Lie algebras, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Vol 682, (2019), 1653-1663.
  • [14] E.S. Ylmaz and K. Ylmaz On Crossed Squares of Commutative Algebras, Math. Sci. Appl. E-Notes, 82, (2020), 32-41.
  • [15] M. Gerstenhaber, A uniform cohomology theory for algebras, Proceedings

QUADRATIC MODULES OF LIE ALGEBRAS FIBRED OVER NIL(2)-MODULES OF LIE ALGEBRAS

Year 2022, , 68 - 75, 31.07.2022

Hatice Taşbozan , Aydın Güzelkokar

https://doi.org/10.33773/jum.1089354

Abstract

In this work we illustrade that the forgetful functor mapping a quadratic module of Lie algebra to a nil(2)-module of Lie algebra is a fibration.

Keywords

Crossed module Lie algebra nil(2)-module Quadratic module

References

  • [1] J.H.C. Whitehead, Combinatorial Homotopy II , Bull. Amer. Math. Soc. 55, 453496, 1949.
  • [2] D.M. Kan, A combinatorial definition of homotopy groups , Annals of Maths. 61, 288312, 1958.
  • [3] D. Conduch, Modules croiss gnraliss de longueur 2, J. Pure and Applied Algebra , 34,(1984), 155-178.
  • [4] G.J.Ellis,Homotopical aspects of Lie algebras, J. Austral. Math. Soc. (Series A),54, (1993), 393-419.
  • [5] A. Grothendieck, Catgories cobress additives et complexe cotangent relatif. In: Lecture Notes in Mathematics, vol. 79. Springer, Berlin (1968).
  • [6] D. Guin-Walery and J-L. Loday, Obsructiona l'excision en K-theorie algebrique, in: Algebraic K-Theory (Evanston 1980). Lecture Notes in Math. (1981), 179-216 (1981).
  • [7] H.J. Baues, Combinatorial homotopy and 4-dimensional complexes, Walter de Gruyter, 15, 1991.
  • [8] I. Aka and Z. Arvasi, Simplicial and crossed Lie algebras, Homology, Homotopy andApplications, Vol. 4 No.(1), (2002) ,43-57.
  • [9] Z. Arvasi and E. Ulualan, : Quadratic and 2-crossed modules of algebras. Algebra Colloquium. (14), 669-686 (2007).
  • [10] E.Ulualan and E.. Uslu, ,Quadratic modules for Lie algebras, Hacettepe Journal of Mathematics and Statistics, Vol40, (3), (2010), 409-419.
  • [11] H. Atik and E. Ulualan,Quadratic modules bibred over nil (2)-modules, Journal of Homotopy and Related Structures, 121, (2017), 83-108.
  • [12] K. Ylmaz,aprazlanm Kareler iin Bir Fibrasyon Uygulamas, Cumhuriyet Science Journal 391, (2018): 1-6.[13] K. Ylmaz and E.S. Ylmaz, Baues cobration for quadratic modules of Lie algebras, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Vol 682, (2019), 1653-1663.
  • [14] E.S. Ylmaz and K. Ylmaz On Crossed Squares of Commutative Algebras, Math. Sci. Appl. E-Notes, 82, (2020), 32-41.
  • [15] M. Gerstenhaber, A uniform cohomology theory for algebras, Proceedings
There are 14 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Hatice Taşbozan 0000-0002-6850-8658

Aydın Güzelkokar 0000-0003-3791-8248

Publication Date July 31, 2022
Submission Date March 17, 2022
Acceptance Date July 21, 2022
Published in Issue Year 2022

Cite

APA Taşbozan, H., & Güzelkokar, A. (2022). QUADRATIC MODULES OF LIE ALGEBRAS FIBRED OVER NIL(2)-MODULES OF LIE ALGEBRAS. Journal of Universal Mathematics, 5(2), 68-75. https://doi.org/10.33773/jum.1089354
AMA Taşbozan H, Güzelkokar A. QUADRATIC MODULES OF LIE ALGEBRAS FIBRED OVER NIL(2)-MODULES OF LIE ALGEBRAS. JUM. July 2022;5(2):68-75. doi:10.33773/jum.1089354
Chicago Taşbozan, Hatice, and Aydın Güzelkokar. “QUADRATIC MODULES OF LIE ALGEBRAS FIBRED OVER NIL(2)-MODULES OF LIE ALGEBRAS”. Journal of Universal Mathematics 5, no. 2 (July 2022): 68-75. https://doi.org/10.33773/jum.1089354.
EndNote Taşbozan H, Güzelkokar A (July 1, 2022) QUADRATIC MODULES OF LIE ALGEBRAS FIBRED OVER NIL(2)-MODULES OF LIE ALGEBRAS. Journal of Universal Mathematics 5 2 68–75.
IEEE H. Taşbozan and A. Güzelkokar, “QUADRATIC MODULES OF LIE ALGEBRAS FIBRED OVER NIL(2)-MODULES OF LIE ALGEBRAS”, JUM, vol. 5, no. 2, pp. 68–75, 2022, doi: 10.33773/jum.1089354.
ISNAD Taşbozan, Hatice - Güzelkokar, Aydın. “QUADRATIC MODULES OF LIE ALGEBRAS FIBRED OVER NIL(2)-MODULES OF LIE ALGEBRAS”. Journal of Universal Mathematics 5/2 (July 2022), 68-75. https://doi.org/10.33773/jum.1089354.
JAMA Taşbozan H, Güzelkokar A. QUADRATIC MODULES OF LIE ALGEBRAS FIBRED OVER NIL(2)-MODULES OF LIE ALGEBRAS. JUM. 2022;5:68–75.
MLA Taşbozan, Hatice and Aydın Güzelkokar. “QUADRATIC MODULES OF LIE ALGEBRAS FIBRED OVER NIL(2)-MODULES OF LIE ALGEBRAS”. Journal of Universal Mathematics, vol. 5, no. 2, 2022, pp. 68-75, doi:10.33773/jum.1089354.
Vancouver Taşbozan H, Güzelkokar A. QUADRATIC MODULES OF LIE ALGEBRAS FIBRED OVER NIL(2)-MODULES OF LIE ALGEBRAS. JUM. 2022;5(2):68-75.