ALGEBRAIC AND HERMITIAN K-THEORY OF kappa-RINGS

作者：Karoubi Max^*; Wodzicki Mariusz

来源：The Quarterly Journal of Mathematics, 2013, 64(3): 903-940.

DOI：10.1093/qmath/hat030

The main purpose of the present article is to establish the real case of %26apos;Karoubi%26apos;s Conjecture%26apos; in algebraic K-theory. The complex case was proved in 1990-91 by Suslin andWodzicki for the C*-algebraic form of the conjecture, and by Wodzicki for both the Banach and C*-algebraic forms. Compared with 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 also be used for complex algebras and provides some simplifications to the original proofs. We also establish a natural analog of Karoubi%26apos;s Conjecture for Hermitian K-theory.

• 出版日期2013-9