Mahanta, Snigdhayan (2015) Algebraic K-theory, K-regularity, and T-duality of O-infinity-stable C*-algebras. MATHEMATICAL PHYSICS ANALYSIS AND GEOMETRY, 18 (1). ISSN 1385-0172, 1572-9656
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We develop an algebraic formalism for topological T-duality. More precisely, we show that topological T-duality actually induces an isomorphism between noncommutative motives that in turn implements the well-known isomorphism between twisted K-theories (up to a shift). In order to establish this result we model topological K-theory by algebraic K-theory. We also construct an E-infinity-operad starting from any strongly self-absorbing C*-algebra D. Then we show that there is a functorial topological K-theory symmetric spectrum construction K-Sigma(top) (-) on the category of separable C*-algebras, such that K-Sigma(top) (D) is an algebra over this operad; moreover, K-Sigma(top) (A (circle times) over cap D) is a module over this algebra. Along the way we obtain a new symmetric spectra valued functorial model for the (connective) topological K-theory of C*-algebras. We also show that O-infinity-stable C*-algebras are K-regular providing evidence for a conjecture of Rosenberg. We conclude with an explicit description of the algebraic K-theory of ax + b-semigroup C*-algebras coming from number theory and that of O-infinity-stabilized noncommutative tori.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | SYMMETRIC SPECTRA; D-BRANES; H-FLUX; CATEGORIES; TOPOLOGY; RINGS; CONJECTURE; HOMOLOGY; EXCISION; MODULES; T-duality; Noncommutative motives; Operads; K-theory; K-regularity; Symmetric spectra |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 31 Jul 2019 09:02 |
| Last Modified: | 31 Jul 2019 09:02 |
| URI: | https://pred.uni-regensburg.de/id/eprint/6253 |
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