Equivalence between Hilbert lattices and quantum dynamic algebras

This talk presents a categorical equivalence between two algebraic quantum structures.  One is the category of Hilbert lattices, where the points of the lattice represent testable properties, and the other is the category of quantum dynamic algebras, where the points of the algebras represent quantum actions.  The value of this equivalence is to clarify how dynamics arises from a seemingly static Hilbert lattice structure.  In this setting, a quantum dynamic algebra that arises from a Hilbert lattice consists of sets of operators on the Hilbert lattice.  Alternative approaches will also be discussed.