Involutions of the second kind for upper triangular matrix algebras

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Let UTn be the algebra of all n × n upper triangular matrices over a field F of characteristic different from 2. In the present work, we will prove that for every automorphism of order 2 on the field F there exists, up to isomorphism, a unique involution of the second kind on UTn whose restriction to F is the given automorphism. As a consequence, the description of involutions of any kind on UTn over a field of characteristic different from 2 is completed.