Approximate biprojectivity and biflatness of some algebras over certain semigroups

We investigate (bounded) approximate biprojectivity of l1(S) for uniformly locally finite inverse semigroups. As a consequence, we show that when S=M(G,I) is the Brandt inverse semigroup, then l1(S) is (boundedly) approximately biprojective if and only if G is amenable. Moreover, we study biflatness and (bounded) approximate biprojectivity of the measure algebra M(S) of a topological Brandt semigroup.