Crossed Products by Semigroups of Endomorphisms and the Toeplitz Algebras of Ordered Groups
Sriwulan Adji, Marcelo Laca, May Nilsen, Iain Raeburn · Proceedings of the American Mathematical Society · 1994
Let ${\Gamma ^ + }$ be the positive cone in a totally ordered abelian group $\Gamma$. We construct crossed products by actions of ${\Gamma ^ + }$ as endomorphisms of ${C^ \ast }$-algebras, and give criteria which ensure a given representation of the crossed product is faithful. We use this to prove that the ${C^\ast }$-algebras generated by two semigroups