Simple Cuntz-Pimsner rings

Identificadores
URI: http://hdl.handle.net/10498/16100
DOI: 10.1016/j.jalgebra.2012.08.005
ISSN: 0021-8693
Files
Statistics
Metrics and citations
Share
Metadata
Show full item recordDate
2012-01-01Department
MatemáticasSource
Journal of Algebra 371 (2012), 367-390Abstract
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, are given. 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.
Subjects
Cuntz–Pimsner rings; Simplicity; Invariant cycles; Condition (L); Cuntz–Krieger uniqueness; Toeplitz rings; Leavitt path algebras; Crossed products; Fractional skew monoid ringsCollections
- Artículos Científicos [4817]
- Articulos Científicos Matemáticas [161]