Characteristic free description of semi-invariants of 2 × 2 matrices

A minimal homogeneous generating system of the algebra of semi-invariants of tuples of two-by-two matrices over an infinite field of characteristic two or over the ring of integers is given. In an alternative interpretation this yields a minimal system of homogeneous generators for the vector invariants of the special orthogonal group of degree four over a field of characteristic two or over the ring of integers. An irredundant separating system of semi-invariants of tuples two-by-two matrices is also determined, it turns out to be independent of the characteristic. © 2019 Elsevier B.V