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

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(ℂ^{n × n}) and is decidable. In contrast, the uniform word problem for the variety generated by all L(ℂ^{n × n}) is shown to be undecidable.