Interior tensor product of Hilbert modules
by
Jan Paseka
Dept. of Mathematics, Masaryk University Brno, Brno, Czech Republic

The lecture is divided in two parts. The first part attempts to begin the investigation of the interior tensor product of Hilbert modules over involutive quantales and establish the basics of this notion. Interior tensor product of Hilbert C*-modules plays a large role in noncommutative topology and geometry. Our idea of the interior tensor product construction is similar as for Hilbert C*-modules and the same is valid for its properties.

To get insight into the structure of Hilbert modules and the involutive quantales representations we explore in the second part of the lecture the notion of Rieffel induction. This gives us, for a right Hilbert A-B bimodule X, a functor Ind-X from the category Rep(B) of non-degenerate representations of an involutive quantale B into Rep(A) of an involutive quantale A. Using this functor we then show that a right A-B bimodule X is an imprimitivity bimodule in the sense of Morita theory if and only if there is a right Hilbert B-A bimodule Y such that the compositions of tensoring functors are equivalent to the respective identity functors.

Date received: May 22, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caee-55.