The generalized Chern character and Lefschetz numbers in W*-modules

Abstract

We define N-theory being some analogue of K-theory on the category of von Neumann algebras such that $K_0(A)\subset N_0(A)$ 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 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.

24 pages, LaTeX 2.09, minor misprint changes

References in corpus (1)

• Lefschetz Numbers and Geometry of Operators in W*-modules

Cited by in corpus (1)

• Hodge decomposition for elliptic complexes over unital $C^{\ast }$-algebras