On Homotopy Theory of Quadratic Modules of Lie Algebras
Yıl 2022,
Cilt: 10 Sayı: 1, 159 - 165, 15.04.2022
Ummahan Ege Arslan
,
Emre Özel
Öz
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.
Destekleyen Kurum
Eskisehir Osmangazi University, Scientific Research Center (BAP)
Kaynakça
- [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.
Yıl 2022,
Cilt: 10 Sayı: 1, 159 - 165, 15.04.2022
Ummahan Ege Arslan
,
Emre Özel
Kaynakça
- [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.