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We generalize a recent construction of Exel and Pardo, from discrete groups acting on finite directed graphs to locally compact groups acting on topological graphs. To each cocycle for such an action, we construct a $C^*$-correspondence whose associated Cuntz-Pimsner algebra is the analog of the Exel-Pardo $C^*$-algebra.
We consider Toeplitz and Cuntz-Krieger $C^*$-algebras associated with finitely aligned left cancellative small categories. We pay special attention to the case where such a category arises as the Zappa-Szep product of a category and a group linked by
We introduce an algebraic version of the Katsura $C^*$-algebra of a pair $A,B$ of integer matrices and an algebraic version of the Exel-Pardo $C^*$-algebra of a self-similar action on a graph. We prove a Graded Uniqueness Theorem for such algebras an
We found that if $u$ and $v$ are any two unitaries in a unital $C^*$-algebra with $|uv-vu|<2$ such that $uvu^*v^*$ commutes with $u$ and $v,$ then the SCA, $A_{u,v}$ generated by $u$ and $v$ is isomorphic to a quotient of the rotation algebra $A_thet
We give the beginnings of the development of a theory of what we call R-coactions of a locally compact group on a $C^*$-algebra. These are the coactions taking values in the maximal tensor product, as originally proposed by Raeburn. We show that the
We define a strong Morita-type equivalence $sim _{sigma Delta }$ for operator algebras. We prove that $Asim _{sigma Delta }B$ if and only if $A$ and $B$ are stably isomorphic. We also define a relation $subset _{sigma Delta }$ for operator algebras.