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Let  UT nbe 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  UT nwhose restriction to  F  is the given automorphism. As a consequence, the description of involutions of any kind on  UT nover a field of characteristic different from 2 is completed.

Involutions of the second kind for upper triangular matrix algebras