On Suslin Matrices and their connection to Spin groups

A concrete representation of the Clifford algebra (for any hyperbolic quadratic space) is given using what are called Suslin matrices. This explicit construction is used to analyze the corresponding Spin groups and the involution and might be of interest in low dimensional computations. Conversely, this connection to Clifford algebras gives a conceptual foundation to some (seemingly accidental) properties of Suslin matrices.
Comment: 2015 paper, improved presentation, 20 pages