Pseudo-amenability of Brandt semigroup algebras
In this paper it is shown that for a Brandt semigroup over a group with an arbitrary index set , if is amenable, then the Banach semigroup algebra is pseudo-amenable.
On the quantum groups and semigroups of maps between noncommutative spaces
We define algebraic families of (all) morphisms which are purely algebraic analogs of quantum families of (all) maps introduced by P. M. Sołtan. Also, algebraic families of (all) isomorphisms are introduced. By using these notions we construct two classes of Hopf-algebras which may be interpreted as the quantum group of all maps from a finite space to a quantum group, and the quantum group of all automorphisms of a finite noncommutative (NC) space. As special cases three classes of NC objects are...
On the differential geometry of some classes of infinite dimensional manifolds
Albeverio, Kondratiev, and Röckner have introduced a type of differential geometry, which we call lifted geometry, for the configuration space of any manifold . The name comes from the fact that various elements of the geometry of are constructed via lifting of the corresponding elements of the geometry of . In this note, we construct a general algebraic framework for lifted geometry which can be applied to various “infinite dimensional spaces” associated to . In order to define a lifted...
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