QUATERNION ALGEBRAS AND INVARIANTS OF VIRTUAL KNOTS AND LINKS I:: THE ELLIPTIC CASE.

In this paper, we show how generalized quaternions including some 2 × 2 matrices, can be used to find solutions of the equation \[ [B,(A - 1)(A,B)] = 0. \] These solutions can then be used to find polynomial invariants of virtual knots and links. The remaining 2 × 2 matrices will be considered in a later paper. [ABSTRACT FROM AUTHOR]