Hermitian Algebraic K-Theory and the Root System D

Abstract

For the root system D, we construct an analog of the Wagoner complex used in his proof of the equivalence of \( {K}_{\ast}^Q \) and \( {K}_{\ast}^{BN} \) (linear) algebraic K-theories. We prove that the corresponding K-theory \( {KU}_{\ast}^D \) for the even orthogonal group is naturally isomorphic to the \( {KU}_{\ast}^{BN} \)-theory constructed by Yu. P. Solovyov and A. I. Nemytov.