Semicrossed Products of Operator Algebras by Semigroups

ISBN-13: 9781470423094 / Angielski

Kenneth R. Davidson;Adam Fuller

Opis

The authors examine the semicrossed products of a semigroup action by $*$-endomorphisms on a C*-algebra, or more generally of an action on an arbitrary operator algebra by completely contractive endomorphisms. The choice of allowable representations affects the corresponding universal algebra. The authors seek quite general conditions which will allow them to show that the C*-envelope of the semicrossed product is (a full corner of) a crossed product of an auxiliary C*-algebra by a group action. Their analysis concerns a case-by-case dilation theory on covariant pairs. In the process we determine the C*-envelope for various semicrossed products of (possibly nonselfadjoint) operator algebras by spanning cones and lattice-ordered abelian semigroups.

Spis treści

• Introduction
• Preliminaries
• Semicrossed products by abelian semigroups
• Nica-covariant semicrosssed products
• Semicrossed products by non-abelian semigroups
• Bibliography.