论文标题
作为同质谎言代数的广义对称性
Generalized symmetries as homotopy Lie algebras
论文作者
论文摘要
同质谎言代数是对给定场理论的运动学和动力学的差分级谎言代数的概括。我们专注于运动学，我们表明这些代数提供了一个自然框架，用于使用两个特定示例来描述广义规格对称性。第一个示例涉及使用对称性hopf代数的drinfel扭曲获得的非交通仪对称性。同型与扭曲的量规对称兼容的代数证明是最近提出的编织l $ _ \ infty $ -Algebra。在第二个示例中，我们着重于双场理论的广义对称性。对称性既包括差异性和规格转换，并且可以使用弯曲的l $ _ \ infty $ -Algebra来始终定义。
Homotopy Lie algebras are a generalization of differential graded Lie algebras encoding both the kinematics and dynamics of a given field theory. Focusing on kinematics, we show that these algebras provide a natural framework for the description of generalized gauge symmetries using two specific examples. The first example deals with the non-commutative gauge symmetry obtained using Drinfel'd twist of the symmetry Hopf algebra. The homotopy Lie algebra compatible with the twisted gauge symmetry turns out to be the recently proposed braided L$_\infty$-algebra. In the second example we focus on the generalized gauge symmetry of the double field theory. The symmetry includes both diffeomorphisms and gauge transformation and can consistently be defined using a curved L$_\infty$-algebra.
