标题： 当前代数和QP流形 显示英文标题

标题： Current Algebras and QP Manifolds

摘要： 由Alekseev和Strobl在二维中引入的广义电流代数通过分次流形和分次泊松括号被重新构造。我们将其广义电流代数推广到高维。QP流形提供了任何维度下电流代数的统一结构。电流代数产生Leibniz/Loday代数胚的结构，这些结构由QP结构表征。特别是，在三维情况下，一个电流代数具有Uchino和一位作者引入的同伦意义下的李代数胚结构，该结构具有Courant-Dorfman括号的推广括号。异常消除条件被重新解释为狄拉克结构的推广。 显示英文摘要

摘要： Generalized current algebras introduced by Alekseev and Strobl in two dimensions are reconstructed by a graded manifold and a graded Poisson brackets. We generalize their current algebras to higher dimensions. QP manifolds provide the unified structures of current algebras in any dimension. Current algebras give rise to structures of Leibniz/Loday algebroids, which are characterized by QP structures. Especially, in three dimensions, a current algebra has a structure of a Lie algebroid up to homotopy introduced by Uchino and one of the authors which has a bracket of a generalization of the Courant-Dorfman bracket. Anomaly cancellation conditions are reinterpreted as generalizations of the Dirac structure.