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Solution of the congruence problem for arbitrary hermitian and skew-hermitian matrices over polynomial rings
Let * be the involutorial automorphism of the complex polynomial algebra C[t] which sends t to -t.Answering a question raised by V.G.Kac, we show that every hermitian or skew-hermitian matrix over this algebra is congruent to the direct sum of 1×1 matrices and 2×2 matrices with zero diagonal.Moreover we show …