Characteristic free description of semi-invariants of $2\times 2$ matrices

Abstract

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 of two-by-two matrices is also determined, it turns out to be independent of the characteristic.

A crucial reference to a paper of A. Lopatin was added

Cited by in corpus (5)

• Separating invariants over finite fields
• Separating invariants of three nilpotent 3x3 matrices
• Separating G_2-invariants of several octonions
• Classification of G_2-orbits for pairs of octonions
• On m-tuples of nilpotent 2x2 matrices over an arbitrary field