Actions of inverse semigroups arising from partial actions of groups

Partial Actions of Inverse and Weakly Left E-ample Semigroups

We introduce partial actions of weakly left E-ample semigroups, thus extending both the notion of partial actions of inverse semigroups and that of partial actions of monoids. Weakly left E-ample semigroups arise very naturally as subsemigroups of partial transformation semigroups which are closed under the unary operation α 7→ α, where α is the identity map on the domain of α. We investigate t...

Partial actions of groups their globalisations and E-unitary inverse semigroups

C-crossed Products by Partial Actions and Actions of Inverse Semigroups

The recently developed theory of partial actions of discrete groups on C-algebras is extended. A related concept of actions of inverse semigroups on C-algebras is defined, including covariant representations and crossed products. The main result is that every partial crossed product is a crossed product by a semigroup action.

Constructing Homomorphisms through E-unitary Inverse Semigroups via Partial Group Actions and Semilattice Actions

Orbit Spaces Arising from Isometric Actions on Hyperbolic Spaces

Let be a differentiable action of a Lie group on a differentiable manifold and consider the orbit space with the quotient topology.  Dimension of is called the cohomogeneity of the action of  on . If is a differentiable manifold  of  cohomogeneity one under the action of  a compact and connected Lie group, then the orbit space is homeomorphic to one of the spaces , , or . In this paper we suppo...