Abstract
We define N-theory as being an analogue of K-theory on the category of von Neumann algebras such that K 0(A)⊂N 0(A) for any von Neumann algebra A. Moreover, it turns out to be possible to construct the extension of the Chern character to some homomorphism from N 0(A) to an even Banach cyclic homology of A. Also, we define generalized Lefschetz numbers for an arbitrary unitary endomorphism U of an A-elliptic complex. We study them in the situation when U is an element of a representation of some compact Lie group.
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Pavlov, A.A. The Generalized Chern Character and Lefschetz Numbers in W*-Modules. Acta Applicandae Mathematicae 68, 137–157 (2001). https://doi.org/10.1023/A:1012299710610
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DOI: https://doi.org/10.1023/A:1012299710610