NK_1 of Bak's unitary group over Graded Rings

TL;DR

This paper investigates the absence of torsion in Bass nil-groups associated with Bak's unitary groups over graded rings, extending classical theory using a graded Quillen--Suslin approach.

Contribution

It introduces a graded version of Quillen--Suslin theory to analyze Bass nil-groups for Bak's unitary groups over graded rings, providing new insights into their torsion properties.

Findings

Demonstrates absence of k-torsion in NK_1GQ(R) for graded rings

Extends classical results to graded ring context

Provides a new framework for analyzing nil-groups in algebraic K-theory

Abstract

For an associative ring $R$ with identity, we study the absence of $k$-torsion in NK_1GQ(R); Bass nil-groups for the general quadratic or Bak's unitary groups. By using a graded version of Quillen--Suslin theory we deduce an analog for the graded rings.