Johnson pseudo-contractibility of certain semigroup algebras. II

Abstract

We investigate Johnson pseudo-contractibility and pseudo-contractibility of Clifford semigroup algebras. We show that, for a Clifford semigroup S, if 1 (S) has a central approximate identity in c 00 (S), then 1 (S) is (Johnson) pseudo-contractible if and only if E(S) is locally finite and each maximal subgroup of S is (amenable) finite, respectively. As an application, we characterize Johnson pseudo-contractibility and pseudo-contractibility of 1 (S), where S is a commutative semigroup, a band semigroup, or an inverse semigroup with totally ordered idempotents set.

Some Characterizations for Approximate Biflatness of Semigroup Algebras

“…Let l 1 (S) be approximately bifat. We regard the l 1 -graded Banach algebra B p � l 1 − ⊕ q∈(p] l 1 (G q ) for all p ∈ E(S) [9]. Obviously, B p is a closed ideal of l 1 (S) and by [9, Proposition 2.1] B p is unital and so Lemma 3 implies that B p is approximately bifat.…”

“…Conversely, let E(S) be locally fnite and every maximal subgroup of S be amenable. Ten, E(S) is well-ordered by [9,Remark 2.10]. Since E(S) is totally ordered, [10,Teorem 16] implies that l 1 (S) has a bounded approximate identity.…”