Hermitian groups and \(K\)-theory
Let \(R\) be a ring with involution \(\bar{\phantom\lambda}\), and let \(\lambda\) be a central element from \(R\), such that \(\lambda \bar{\lambda} = 1\). The author studies the functors \(K_1\) and \(K_2\) of the category of non-singular \(\lambda\)-Hermitian spaces on finitely generated projective \(R\)-modules in the framework of the theory of \(\Lambda\)-quadratic modules developed by \textit{A. Bak} [cp. ``\(K\)-theory of forms'', Ann. Math. Stud. 98 (1981; Zbl 0465.10013)]. In particular, the elementary subgroup of the general Hermitian group and the Hermitian Steinberg group are defined, and it is shown that the Hermitian Whitehead lemma holds and that the Hermitian Steinberg group is the universal central extension of the elementary subgroup of the general Hermitian group in analogy with the linear and the quadratic case.
scientific article; zbMATH DE number 1139538