Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1898722 | Journal of Geometry and Physics | 2011 | 15 Pages |
Abstract
Quillen introduced a new K0â²-theory of nonunital rings in Quillen (1996) [1] and showed that, under some assumptions (weaker than the existence of unity), this new theory agrees with the usual algebraic K0alg-theory. For a field k of characteristic 0, we introduce higher nonunital K-theory of k-algebras, denoted as KQ, which extends Quillen's original definition of the K0â² 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 Câ-algebras. The machinery enables us to produce a DG categorical formalism of topological homological T-duality using bivariant K-theory classes. A connection with strong deformations of Câ-algebras and some other potential applications to topological field theories are discussed towards the end.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Snigdhayan Mahanta,