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： Alekseev 和 Strobl 在二维引入的广义电流代数通过一个分级流形和一个分级泊松括号被重构。 我们将他们的电流代数推广到更高维度。 QP 流形为任意维度的电流代数提供了统一结构。 电流代数产生了李-莱布尼兹/Loday 代数胚的结构，这些结构由 QP 结构刻画。 特别是，在三维情况下，电流代数具有 Uchino 和本文一位作者引入的同伦意义上的李代数胚结构，该结构的括号是 Courant-Dorfman 括号的推广。 异常消除条件被重新解释为 Dirac 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.