Normality of Vaserstein group

TL;DR

This paper extends the normality theorem for Vaserstein groups, generalizing previous results for symplectic groups associated with any invertible skew-symmetric matrix of Pfaffian one, within the context of projective modules.

Contribution

The paper proves a normality theorem for Vaserstein groups associated with any invertible skew-symmetric matrix of Pfaffian one, broadening prior results.

Findings

Established normality of Vaserstein groups for general skew-symmetric matrices.

Extended Kopeiko's results from standard to arbitrary invertible skew-symmetric matrices.

Generalized the normality theorem to the setting of projective modules.

Abstract

A.A. Suslin proved a normality theorem for an elementary linear group and V.I. Kopeiko extended this result of Suslin for a symplectic group defined with respect to the standard skew-symmetric matrix of even size. We generalized the result of Kopeiko for a symplectic group defined with respect to any invertible skew-symmetric matrix of Pfaffian one. Vaserstein group is an extension of a symplectic group defined with respect to any invertible skew-symmetric matrix of Pfaffian one in the set up of projective modules. Here we prove a normality theorem for Vaserstein group.