Homotopy theory of complete Lie algebras and Lie models of simplicial sets55P62 (primary)17B5555U10 (secondary)In a previous work, by extending the classical Quillen construction to the non-simply connected case, we have built a pair of adjoint functors, model and realization,between the ...
By integrating the Lie quasi-bialgebroid associated to the Courant algebroid, we obtain a Lie-quasi-Poisson groupoid from a $2$-term $L_\infty$-algebra, which is proposed to be the geometric structure on the dual of a Lie $2$-algebra. These results lead to a construction of a new 2...
We classify strongly homotopy Lie algebras—also called L ∞ algebras—of one even and two odd dimensions, which are related to 2 | 1-dimensional Z 2-graded Lie algebras. What makes this case interesting is that there are many nonequivalent L ∞ examples, in addition to the Z 2-graded ...
1. Definitions and statements of results 1.1. Holonomy and homotopy Lie algebras. Fix a field k of characteristic 0. Let A be a graded, graded-commutative algebra over k, with graded piece A k , k ≥ 0. We will assume throughout that A is locally finite, connected, and generated...
Poinkales topology and Hilberts algebraic geometry, like Plancks quantum theory and Einsteins theory of relativity, revolutionized the basic idea of the whole subject. This post tried to introduce the two concepts introduced by poinkale: homology group and basic group. They are algebraic ...
Quantization of strongly homotopy Lie bialgebras 来自 Semantic Scholar 喜欢 0 阅读量: 41 作者: SA Merkulov 摘要: Using theory of props we prove a formality theorem associated with universal quantizations of (strongly homotopy) Lie bialgebras.关键词:...
which exhibits the gauge group Gi,k as the homotopy fibre of the map ∂i,k. This is a key observation, as it suggests that the homotopy theory of the gauge groups Gi,k depends on the maps ∂i,k. In fact, more is true. By [15, Theorem 2.6], the adjoint of ∂i,k:PU(n...
s construction of a homotopy Lie algebra associated with the holomorphic tangent bundle of a complex manifold, we prove that the space of vector fields on a dg manifold admits anL∞[1]algebra structure, unique up to isomorphism, whose unary bracket is the Lie derivative with respect to the ...
Berglund A.: Rational homotopy theory of mapping spaces via Lie theory for \(L_\infty \) -algebras, Arxiv, preprint, arXiv:1110.6145v1 (2011)A. Berglund, Rational homotopy theory of mapping spaces via Lie theory for L∞-algebras, Homology Homotopy Appl. 17 (2015), no.2, 343-369....
series of homotopy lie algebras and poincar e algebras with monomial relationsAvramov, Luchezar L