2011/01/04 by Snigdhayan Mahanta · 6 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Algebra over a field #Algebraic structures and combinatorial models #Cohomology #Combinatorics #Field (mathematics) #Functor #Homotopy and Cohomology in Algebraic Topology #Idempotence #K-theory (physics) #Knot theory #Mathematics #Physics #Pure mathematics #Topology (electrical circuits) #math-ph #math.KT #math.MP #msc:19Dxx #msc:46L85 #msc:57R56 #msc:58B34
paper · pdf · doi:10.1016/j.geomphys.2010.12.011
published in Journal of Geometry and Physics 61(5), 875-889 (Elsevier BV) · 24 pages, the manuscript of an article published in 2011. arXiv admin note: text overlap with arXiv:0906.5400
openalex publication_date 2011/01/04 · arxiv created 2015/03/22 · arxiv updated 2015/03/29 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Quillen introduced a new K'0-theory of nonunital rings and showed that, under some assumptions (weaker than the existence of unity), this new theory agrees with the usual algebraic Kalg0-theory. For a field k of characteristic 0, we introduce higher nonunital K-theory of k-algebras, denoted KQ, which extends Quillen's original definition of the K'0 functor. We show that the KQ-theory is Morita invariant and satisfies excision connectively, in a suitable sense, on the category of idempotent k-algebras. Using these two properties we show that the KQ-theory agrees with the topological K-theory of stable C^*-algebras. The machinery enables us to produce a DG categorical formalism of topological homological \mathbbT-duality using bivariant K-theory classes. A connection with strong deformations of C^*-algebras and some other potential applications to topological field theories are discussed towards the end.