Natsume-Olsen球面上的一个非交换Borsuk-Ulam定理
A Noncommutative Borsuk-Ulam Theorem for Natsume-Olsen Spheres
摘要：
Natsume-Olsen非交换球是C*-代数，当k是奇数时，它推广了C（S^k）。这些代数允许有限循环群的自然作用，并且如果这些作用之一是固定的，则相同维数的两个Natsume-Olsen球面之间的任何等变同态在奇K-理论上诱导出非平凡映射。这个结果是一个推广的、非交换的奇维Borsuk-Ulam定理，并且正如在拓扑情况下一样，这个定理在任意维的θ-变形球面上有许多（几乎）等价的公式。此外，受A. Borsuk-Ulam的代数结果的启发，我们给出了分次巴拿赫代数的定理。塔哈维
英文摘要：
Natsume-Olsen noncommutative spheres are C*-algebras which generalize C(S^k) when k is odd. These algebras admit natural actions by finite cyclic groups, and if one of these actions is fixed, any equivariant homomorphism between two Natsume-Olsen spheres of the same dimension induces a nontrivial map on odd K-theory. This result is an extended, noncommutative Borsuk-Ulam theorem in odd dimension, and just as in the topological case, this theorem has many (almost) equivalent formulations in terms of theta-deformed spheres of arbitrary dimension. In addition, we present theorems on graded Banach algebras, motivated by algebraic Borsuk-Ulam results of A. Taghavi.
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