Partial-isometric crossed products of dynamical systems by left LCM semigroups

Let P be a left LCM semigroup, and α an action of P by endomorphisms of a C ∗ -algebra A. We study a semigroup crossed product C ∗ -algebra in which the action α is implemented by partial isometries. This crossed product gives a model for the Nica-Teoplitz algebras of product systems of Hilbert bimodules (associated with semigroup dynamical systems) studied first by Fowler, for which we provide a structure theorem as it behaves well under short exact sequences and tensor products.