On the Cohomology of Joins of Operator Algebras
Author | : Ali-Amir Husain |
Publisher | : |
Total Pages | : |
Release | : 2004 |
ISBN-13 | : OCLC:712673747 |
ISBN-10 | : |
Rating | : 4/5 ( Downloads) |
Download or read book On the Cohomology of Joins of Operator Algebras written by Ali-Amir Husain and published by . This book was released on 2004 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The algebra of matrices M with entries in an abelian von Neumann algebra is a C*-module. C*-modules were originally defined and studied by Kaplansky and we outline the foundations of the theory and particular properties of M. Furthermore, we prove a structure theorem for ultraweakly closed submodules of M, using techniques from the theory of type I finite von Neumann algebras. By analogy with the classical join in topology, the join for operator algebras A and B acting on Hilbert spaces H and K, respectively, was defined by Gilfeather and Smith. Assuming that K is finite dimensional, Gilfeather and Smith calculated the Hochschild cohomology groups of the join. We assume that M is the algebra of matrices with entries in a maximal abelian von Neumann algebra U, A is an operator algebra acting on a Hilbert space K, and B is an ultraweakly closed subalgebra of M containing U. In this new context, we redefine the join, generalize the calculations of Gilfeather and Smith, and calculate the cohomology groups of the join.