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

For a nite 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. This is a report on joint work with Luca Giudici. A few remarks, based on joint work with Martin Ziegler, on the complexity of the decidable problem will be added.