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The left regular *-representation of an inverse semigroup

The left regular *-representation of an inverse semigroup

The left regular <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="Superscript asterisk"> <mml:semantics> <mml:msup> <mml:mi /> <mml:mo>∗<!-- ∗ --></mml:mo> </mml:msup> <mml:annotation encoding="application/x-tex">^ *</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-representation of the semigroup algebra of an inverse semigroup is faithful. Clifford semigroups with a particular type of semilattice are shown to have the weak containment property if …