From simplicial Lie algebras and hypercrossed complexes to differential graded Lie algebras via 1-jets

Preprint English OPEN
Jurco, Branislav;
(2011)
  • Related identifiers: doi: 10.1016/j.geomphys.2012.09.002
  • Subject: Mathematical Physics | Mathematics - Differential Geometry
    arxiv: Mathematics::Algebraic Topology | Mathematics::Category Theory

Let g be a simplicial Lie algebra with Moore complex Ng of length k. Let G be the simplicial Lie group integrating g, which is simply connected in each simplicial level. We use the 1-jet of the classifying space of G to construct, starting from g, a Lie k-algebra L. The... View more
  • References (23)
    23 references, page 1 of 3

    [1] P. Aschieri, L. Cantini, B. Jurˇco, Nonabelian Bundle Gerbes, their Differential Geometry and Gauge Theory, Commun.Math.Phys. 254 (2005) 367

    [2] M. Alexandrov, M. Kontsevich, A. Schwarz and O. Zaboronsky, The Geometry of the Master Equation and Topological Quantum Field Theory, Int. J. Mod. Phys. A12 (1997) 1405-1429.

    [3] I˙. Ak¸ca, Z. Arvasi, Simplicial and crossed Lie algebras, Homology Homotopy Appl. 4 (2002) 43-5

    [4] Z. Arvasi, T.S. Kuzpinari, E.O¨ . Uslu, Three Crossed Modules, arXiv:0812.4685 [math.CT].

    [5] J. C. Baez, A. S. Crans, Higher-Dimensional Algebra VI: Lie 2-Algebras, Theor. Appl. Categor. 12 (2004) 492-528.

    [6] P. Carrasco, A. M. Cegarra, Group theoretic algebraic models for homotopy types, J. Pure Appl. Algebra 75(1991) 195-235.

    [7] D. Conduch´e, Modules crois´es g´eneralis´es de longeur 2, J. Pure Appl. Algebra 34 (1984) 155-178.

    [8] E. Curtis, Simplicial Homotopy Theory, Advances in Math. 6 (1971) 107-209

    [9] J. L. Dupont, Curvature and characteristic classes, LNM 640, Springer 1978

    [10] J. Duskin, Simplicial matrices and the nerves of weak n-categories I: nerves of bicategories, Theor. Appl. Categor. 9 (2002) 198-308.

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