Higher nonunital Quillen K′ -theory, KK -dualities and applications to topological -dualities
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- 作者：Snigdhayan Mahanta ; a ; snigdhayan.mahanta@adelaide.edu.au
- 关键词： ; none ; color ; black"" href=""/science?_ob=MathURL&_method=retrieve&_udi=B6TJ8-51VB7WM-1&_mathId=mml20&_user=1019048&_cdi=5304&_pii=S0393044010002627&_rdoc=2&_issn=03930440&_acct=C000053065&_version=1&_userid=14894
- 刊名：Journal of Geometry and Physics
- 出版年：2011
- 出版时间：May 2011
- 年：2011
- 卷：61
- 期：5
- 页码：875-889
- 全文大小：360 K
文摘
Quillen introduced a new -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 -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 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 -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.