BIRS Workshop Lecture Videos
Simple Cuntz-Pimsner rings Ortega, Eduard
Together with Carlsen we Introduced the Cuntz-Pimsner rings, a pure algebraic analog of the Cuntz-Pimsner algebras. We showed that they generalized, for example, the crossed products and the Leavitt path algebras. In this talk we are going to give necessary and sufficient conditions for when every non-zero ideal in a relative Cuntz-Pimsner ring contains a non-zero graded ideal, when a relative Cuntz- Pimsner ring is simple, and when every ideal in a relative Cuntz-Pimsner ring is graded. A “Cuntz-Krieger uniqueness theorem” for relative Cuntz-Pimsner rings is also given and Condition (L) and Condition (K) for relative Cuntz-Pimsner rings are introduced. As applications of these results, a uniqueness result for the Toeplitz algebra of a directed graph and characterizations of when crossed products of a ring by a single automorphism and fractional skew monoid rings of a single corner isomorphism are simple, are obtained. This is a joint work with T.M.Carlsen and E.Pardo.
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