English

Algebraic and Hermitian K-theory of K-rings

K-Theory and Homology 2013-10-16 v1

Abstract

The main purpose of the present article is to establish the real case of "Karoubi's conjecture" in algebraic K-theory. The complex case was proved in 1990-91 by the second author and Andrei Suslin. Compared to the case of complex algebras, the real case poses additional difficulties. This is due to the fact that topological K-theory of real Banach algebras has period 8 instead of 2. The method we employ to overcome these difficulties can be used for complex algebras, and provides some simplifications to the original proofs. We also establish a natural analog of "Karoubi's conjecture" in Hermitian K-theory.

Keywords

Cite

@article{arxiv.1310.4123,
  title  = {Algebraic and Hermitian K-theory of K-rings},
  author = {Max Karoubi and Mariusz Wodzicki},
  journal= {arXiv preprint arXiv:1310.4123},
  year   = {2013}
}

Comments

33 pages, to be published in a special issue of the Quarterly Journal of Math., dedicated to D. Quillen