Fundamental property of $$2 \times n$$ row Suslin matrices

Abstract

The study of unimodular rows over a commutative ring involves the utilization of Suslin matrices. These matrices possess a Fundamental Property, which plays a crucial role in establishing connections between the group generated by special Suslin matrices and the special orthogonal group. Moreover, the Fundamental Property serves as a means to establish a link between Suslin matrices and Spin groups. In this work, we focus on \(2 \times n\) row Suslin matrices, defining them and exploring their properties. We provide a proof for the Fundamental Property specific to \(2 \times n\) row Suslin matrices.