$K_0$ of purely infinite simple regular rings
By P. Ara, K. Goodearl, Enrique Pardo. 2001
99 citations recorded by the source corpus.
We extend the notion of a purely infinite simple C*-algebra to the context of unital rings, and we study its basic properties, specially those related to K-Theory. For instance, if $R$ is a purely infinite simple ring, then $K_0(R)^+= K_0(R)$, the monoid of isomorphism classes of finitely generated projective $R$-modules is isomorphic to the monoid obtained from $K_0(R)$ by adjoining a new zero element, and $K_1(R)$ is the abelianization of the group of units of $R$. We develop techniques of construction, obtaining new examples in this class in the case of von Neumann regular rings, and we compute the Grothendieck groups of these examples. In particular, we prove that every countable abelian group is isomorphic to $K_0$ of some purely infinite simple regular ring. Finally, some known examples are analyzed within this framework.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/6ffa5e20b72cde940482ade86e04d42068e11802
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In Algebra and Number Theory
- G. Abrams
- G. Pino
- M. Tomforde
- Iain Raeburn
- Astrid an Huef
- John Clark
- Roozbeh Hazrat
- Mercedes Siles Molina
In Geometry and Topology
In Mathematical Physics
- G. Abrams
- G. Pino
- M. Tomforde
- Astrid an Huef
- John Clark
- Iain Raeburn
- Roozbeh Hazrat
- Mercedes Siles Molina
Citations in the corpus
- Leavitt path algebras: the first decade (2014, background): “Purely infinite simple rings were first introduced in [35]; the idea was born in the context of C-algebras.”
- Kumjian-Pask algebras of higher-rank graphs (2011, background): “If Λ is cofinal and {o(e) : e ∈ Λ1} is unbounded, then KPC(Λ) is not purely infinite in the sense of [4].”