Presentations of Semigroup Algebras of Weighted Trees

Weighted Convolution Measure Algebras Characterized by Convolution Algebras

The weighted semigroup algebra Mb (S, w) is studied via its identification with Mb (S) together with a weighted algebra product *w so that (Mb (S, w), *) is isometrically isomorphic to (Mb (S), *w). This identification enables us to study the relation between regularity and amenability of Mb (S, w) and Mb (S), and improve some old results from discrete to general case.

Gorenstein Semigroup Algebras of Weighted Trees

We classify exactly when the toric algebras C[ST (r)] are Gorenstein. These algebras arise as toric deformations of algebras of invariants of the Cox-Nagata ring of the blow-up of n − 1 points on P, or equivalently algebras of the ring of global sections for the Plücker embedding of weight varieties of the Grassmanian Gr2(Cn), and algebras of global sections for embeddings of moduli of weighted...

$sigma$-Connes Amenability and Pseudo-(Connes) Amenability of Beurling Algebras

In this paper,  pseudo-amenability and pseudo-Connes amenability of weighted semigroup algebra $ell^1(S,omega)$ are studied. It is proved that pseudo-Connes amenability and pseudo-amenability of weighted group algebra $ell^1(G,omega)$ are the same. Examples are given to show that the class of $sigma$-Connes amenable dual Banach algebras is larger than that of Connes amenable dual Banach algebras.

Derivations on Certain Semigroup Algebras

In the present paper we give a partially negative answer to a conjecture of Ghahramani, Runde and Willis. We also discuss the derivation problem for both foundation semigroup algebras and Clifford semigroup algebras. In particular, we prove that if S is a topological Clifford semigroup for which Es is finite, then H1(M(S),M(S))={0}.

First Order Cohomology of l^1-Munn Algebras and Certain Semigroup Algebras