Chiral equivariant cohomology II
Chiral equivariant cohomology II
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手性等变上同调 II
DOI：
10.1090/s0002-9947-08-04504-2
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发表时间：
2006
影响因子：
1.3
通讯作者：
Bailin Song
中科院分区：
文献类型：
--
作者：
B. Lian;A. Linshaw;Bailin Song
这是关于在顶点代数中取值的新等变上同调的系列论文中的第二篇。在较早的一篇论文中，前两位作者给出了 O(sg) 代数范畴上同调函子的构造。新的上同调理论可以被视为经典等变上同调的一种“手性化”，后者是在 H. Cartan 的 G* 代数范畴上定义的。在本文中，我们进一步发展手性理论，首先将其扩展为允许更大的代数类，我们称之为 sg[t] 代数。在几何设置中，O(sg) 代数的主要例子是 G 流形 M 的手性 de Rham 复数 Q(M)。 Q(M) 有一个有趣的子代数，它不承认完整的 O(sg) 代数结构，但保留了 sg[t] 代数的结构，足以让我们定义其手性等变上同调。后者被证明具有许多令人惊讶的特征，使我们能够描绘 G 流形 M 的许多有趣的几何方面，有时以与经典理论完全不同的方式。
This is the second in a series of papers on a new equivariant cohomology that takes values in a vertex algebra. In an earlier paper, the first two authors gave a construction of the cohomology functor on the category of O(sg) algebras. The new cohomology theory can be viewed as a kind of "chiralization" of the classical equivariant cohomology, the latter being defined on the category of G* algebras a la H. Cartan. In this paper, we further develop the chiral theory by first extending it to allow a much larger class of algebras which we call sg[t] algebras. In the geometrical setting, our principal example of an O(sg) algebra is the chiral de Rham complex Q(M) of a G manifold M. There is an interesting subalgebra of Q(M) which does not admit a full O(sg) algebra structure but retains the structure of an sg[t] algebra, enough for us to define its chiral equivariant cohomology. The latter then turns out to have many surprising features that allow us to delineate a number of interesting geometric aspects of the G manifold M, sometimes in ways that are quite different from the classical theory.