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Characteristic free description of semi-invariants of 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 of two-by-two matrices is also determined, it turns
out to be independent of the characteristic.Comment: A crucial reference to a paper of A. Lopatin was adde
Defining relation for semi-invariants of three by three matrix triples
The single defining relation of the algebra of -invariants
of triples of matrices is explicitly computed. Connections to some
other prominent algebras of invariants are pointed out.Comment: 12 page
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