Graded K-theory for Z_2-graded graph C*-algebras

Abstract: While there is no universally agreed-upon definition of Z_2-graded K-theory for C*-algebras, a very natural way to define it is using Kasparov's celebrated KK-bifunctor: KK is naturally a Z_2-graded theory, and Kasparov proved that if applied to trivially-graded C*-algebras A, the groups KK_*(\mathbb{C}, A) are the K-groups of A. So it is natural to define K^{gr}_*(A) as KK_*(\mathbb{C}, A) for Z_2-graded C*-algebras A in general. I will discuss recent work with Adam Sierakowski and with honours students Quinn Patterson and Jonathan Taylor, building on previous work with Kumjian and Pask, that uses deep ideas of Pimsner to compute the graded K-theory, defined in this way, of relative graph C*-algebras carrying Z_2-gradings determined by binary labellings of the edges of the graph: the formulas that emerge strongly suggest that this notion of graded K-theory captures the right sort of information.

operator algebrasrings and algebras

Audience: researchers in the topic

Western Sydney University Abend Seminars

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