Universal central extensions of linear groups over rings of non-commutative Laurent polynomials, associated $K_1$-groups and $K_2$-groups

Abstract

We prove that linear groups over rings of non-commutative Laurent polynomials $D_{\tau }$ have Tits systems with the corresponding affine Weyl groups and have universal central extensions if $|Z(D)|\ge 5$ and $|Z(D)|\ne 9$. We also determine structures of $K_1$-groups and identify generators of $K_2$-groups.

22pages