The semigroup algebra and representations of a compact simple semigroup

AnL1algebra for linearly quasi-ordered compact semigroups

“…Before we begin the study of the semigroups in the title, we wish to point out the differences in the measures discussed here and the L 1 algebra constructed here with those found in such papers as [3], [4], [7], [9], [10] and [11]. It is shown in [11] that "r*-invariant" measures on compact semigroups are supported on the minimal ideal of such semigroups.…”

“…The measures used here will have support outside the minimal ideal. The work in [4] on compact simple semigroups reduces to the compact group situation in commutative semigroups and thus there is no relation to our work. In [3], the use of idempotent measures insures that the support is an ideal, again distinct from the situation here.…”