论文标题
从Euler元素和3年级到非紧密因果对称空间
From Euler elements and 3-gradings to non-compactly causal symmetric spaces
论文作者
论文摘要
在本文中，我们讨论了对称空间的因果结构与代数量子场理论（AQFT）的几何方面之间的相互作用。中心焦点是谎言代数中的欧拉元素集，即伴随动作定义3级的元素。在本文的上半年中，我们从Euler元素的角度研究了还原性因果对称空间的分类。这种观点是由AQFT最近应用的动机。在下半年，我们获得了几个结果，可以准备探索因果对称空间和AQFT结构之间的更深层次的联系。特别是，我们探讨了强烈的正交根和SL_2-囊膜的相应系统的技术。此外，我们在Euler元素的伴随轨道中表现出真实的Matsuki冠，并描述了Euler元素稳定器组的连接组件组。
In this article we discuss the interplay between causal structures of symmetric spaces and geometric aspects of Algebraic Quantum Field Theory (AQFT). The central focus is the set of Euler elements in a Lie algebra, i.e., elements whose adjoint action defines a 3-grading. In the first half of this article we survey the classification of reductive causal symmetric spaces from the perspective of Euler elements. This point of view is motivated by recent applications in AQFT. In the second half we obtain several results that prepare the exploration of the deeper connection between the structure of causal symmetric spaces and AQFT. In particular, we explore the technique of strongly orthogonal roots and corresponding systems of sl_2-subalgebras. Furthermore, we exhibit real Matsuki crowns in the adjoint orbits of Euler elements and we describe the group of connected components of the stabilizer group of Euler elements.
