Homotopies of Crossed Modules of Lie Algebras
Year 2018,
Volume: 6 Issue: 2, 259 - 263, 15.10.2018
İbrahim İlker Akça
,
Yavuz Sidal
Abstract
In this paper we will define a notion of homotopy of Lie crossed module morphisms. Then we construct a groupoid structure of Lie crossed module morphisms and their homotopies.
References
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[1] AKCA, I.I. - EMIR, K. - MARTINS, J.F. Pointed Homotopy of Between 2-Crossed Modules of Commutative Algebras, Homology, Homotopy and
Applications vol.17(2) pages 1-30, (2015).
-
[2] BROWN, R. AND HIGGINS P. J., Tensor Products and Homotopies for wgroupoids and crossed complexes, Journal of Pure and Applied Algebra 47,
(1987), 1-33.
-
[3] CABELLO, J.G. AND GARZON A.R. Closed model structures for algebraic models of n-types, Journal of Pure and Applied Algebra 103 (3), (1995),
287–302.
-
[4] DWYER, W.G. - SPALINSKI, J. Homotopy theories and model categories, In Handbook of algebraic topology, pages 73-126. Amsterdam: Nort Holland,
(1995)
-
[5] GOHLA, B. - MARTINS, J.F. Pointed Homotopy and Pointed Lax Homotopy of 2-Crossed Module Maps, Adv. Math. 248: pages 986-1049, (2013).
-
[6] KASEL, C. and LODAY, J.L. Extensions centrales d’algebres de Lie. Ann. Inst. Fourier (Grenoble), 33, (1982) 119-142.
-
[7] NOOHI, B. Notes on 2-groupoids, 2-groups and crossed modules, Homology Homotopy Appl. 9 (1), (2007), 75-106.
-
[8] WHITEHEAD, J.H.C. Combinatorial Homotopy I and II, Bull. Amer. Math. Soc., 55, 231-245 and 453-456 (1949).
Year 2018,
Volume: 6 Issue: 2, 259 - 263, 15.10.2018
İbrahim İlker Akça
,
Yavuz Sidal
References
-
[1] AKCA, I.I. - EMIR, K. - MARTINS, J.F. Pointed Homotopy of Between 2-Crossed Modules of Commutative Algebras, Homology, Homotopy and
Applications vol.17(2) pages 1-30, (2015).
-
[2] BROWN, R. AND HIGGINS P. J., Tensor Products and Homotopies for wgroupoids and crossed complexes, Journal of Pure and Applied Algebra 47,
(1987), 1-33.
-
[3] CABELLO, J.G. AND GARZON A.R. Closed model structures for algebraic models of n-types, Journal of Pure and Applied Algebra 103 (3), (1995),
287–302.
-
[4] DWYER, W.G. - SPALINSKI, J. Homotopy theories and model categories, In Handbook of algebraic topology, pages 73-126. Amsterdam: Nort Holland,
(1995)
-
[5] GOHLA, B. - MARTINS, J.F. Pointed Homotopy and Pointed Lax Homotopy of 2-Crossed Module Maps, Adv. Math. 248: pages 986-1049, (2013).
-
[6] KASEL, C. and LODAY, J.L. Extensions centrales d’algebres de Lie. Ann. Inst. Fourier (Grenoble), 33, (1982) 119-142.
-
[7] NOOHI, B. Notes on 2-groupoids, 2-groups and crossed modules, Homology Homotopy Appl. 9 (1), (2007), 75-106.
-
[8] WHITEHEAD, J.H.C. Combinatorial Homotopy I and II, Bull. Amer. Math. Soc., 55, 231-245 and 453-456 (1949).