ON WEAK AMENABILITY OF RESTRICTED SEMIGROUP ALGEBRA AND SEMIGROUP ALGEBRA ON RESTRICTED SEMIGROUP
Keywords:
semigroup, restricted semigroup, semigroup algebra, weakly amenable.Abstract
We studied weak amenability of restricted semigroup algebra and semigroup algebra l1(Sr), on restricted semigroup Sr. We give condition for the restricted semigroup algebra to be commutative for every inverse semigroup S. Some classes of inverse semigroups such as semilattice, Clifford and Brandt semigroup are used to characterize a weakly amenable restricted semigroup algebra. In particular, we show that for a Clifford semigroup S = Gi and the Brandt semigroup S = M0(G, I, n), the weak amenability of semi- group algebra l1(S), restricted semigroup algebra l1(S), and semigroup algebra l1(Sr), on restricted semigroup Sr are equivalent. In general, the necessary and sufficient conditions for weak amenability of restricted semigroup algebra and semigroup algebra l1(Sr), on restricted semigroup Sr are given.
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