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Simple Cuntz-Pimsner rings Ortega, Eduard
Description
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.
Item Metadata
Title |
Simple Cuntz-Pimsner rings
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2013-04-25
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Description |
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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Extent |
62 minutes
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: University of Trondheim (NTNU)
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Series | |
Date Available |
2014-08-07
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivs 2.5 Canada
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DOI |
10.14288/1.0043525
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Postdoctoral
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivs 2.5 Canada