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On the equational theory of projection lattices of finite von neumann factors

Published online by Cambridge University Press:  12 March 2014

Christian Herrmann
Christian Herrmann*
Affiliation:
Technische Universität Darmstadt, Fb Mathematik, Schlossgartenstr. 7, D 64289 Darmstadt, Germany. E-mail: herrmann@mathematik.tu-darmstadt.de
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Abstract

For a finite von Neumann algebra factor M, the projections form a modular ortholattice L(M). We show that the equational theory of L(M) coincides with that of some resp. all L(ℂn×n ) and is decidable. In contrast, the uniform word problem for the variety generated by all L(ℂn×n) is shown to be undecidable.

Keywords

von Neumann algebraprojection latticecontinuous geometryequational theory

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 75 , Issue 3 , September 2010 , pp. 1102 - 1110
Copyright
Copyright © Association for Symbolic Logic 2010

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