A conjugacy criterion for two pairs of 2 x 2 matrices over a commutative ring (Bogdan Petrenko, Eastern Illinois University)

I will explain how to apply presentations of algebras (together with some classical results from non-commutative algebra) to obtain some 5 polynomial invariants telling us when two pairs of 2×2 matrices over a commutative ring are conjugate, assuming that each of these pairs generate the matrix algebra. This talk is based on my joint paper with Marcin Mazur (Binghamton University):  Separable algebras over infinite fields are 2-generated and finitely presented, Arch. Math. 93 (2009), 521-529.