C*-algebras associated with integral domains and crossed products by actions on adele spaces
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We compute the K-theory for C*-algebras naturally associated with rings of integers in number fields. The main ingredient is a duality theorem for arbitrary global fields. It allows us to identify the crossed product arising from affine transformations on the finite adeles with the analogous crossed product algebra over the infinite adele space.
Subfields: Algebra and Number Theory, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/a7d2b84feaf68ed25381a430f6e67a2580ae7c3a
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In Algebra and Number Theory
In Mathematical Physics
Citations in the corpus
- Nuclearity of semigroup C*-algebras and the connection to amenability (2012, background): “XIN LI connection between nuclearity and faithfulness of the left regular representation remained mysterious. Recently, new examples of C*-algebras arising from number theory ([Cun], [Cu-Li1], [Li1], [Cu-Li2]) have motivated the author to generalize A. Nica’s work. For semigroups associated with num”
- On the K-theory of the C*-algebra generated by the left regular representation of an Ore semigroup (2012, methodology): “(z+I)(C∗ r(R⋊R×)/I)(z+I) which is Murray-von Neumann equivalent to δ+I, hence properly infinite itself. Combining Theorem 8.2.1 and Theorem 8.2.4 with the K-theoretic results for ring C*-algebras from [Cu-Li] and [Li-Lu¨], we obtain K-THEORY OF SEMIGROUP C*-ALGEBRAS 43 Corollary 8.2.11. For every rin”