论文标题
Boutet de Monvel符号代数
Equivariant cyclic cocycles on the Boutet de Monvel symbol algebra
论文作者
论文摘要
我们在Boutet de Monvel运算符的符号代数上构建一个周期性的环状合过程，并使用它来解释Fedosov作为Chern-Connes对$ k $ - 与此环状囊性的椭圆形符号中的chern-connes配对的椭圆形相差的边界价值问题的索引公式。我们还考虑了模棱两可的案例。也就是说，我们在符号的代数的交叉产物上构建了一个周期性的循环共生，由自动形态作用在该代数上。此类交叉产品在转移运算符的非本地边界价值问题的索引理论中。
We construct a periodic cyclic cocycle on the symbol algebra of Boutet de Monvel operators and use it to interpret the index formula for elliptic pseudodifferential boundary value problems due to Fedosov as the Chern--Connes pairing of the classes in $K$-theory of elliptic symbols with this cyclic cocycle. We also consider the equivariant case. Namely, we construct a periodic cyclic cocycle on the crossed product of the algebra of symbols with a group acting on this algebra by automorphisms. Such crossed products arize in index theory of nonlocal boundary value problems with shift operators.
