Involutionen zweiter Art in halbeinfachen Algebren. (Involutions of the second kind in semisimple algebras)
Let A be a finite-dimensional semismiple algebra over an algebraically closed field K. This article describes all involutions * of A that act non-trivially on K (called involutions of the second kind). If A is simple, \(A=M_ n(K)\) say, and \({}^-\) denotes the map that transforms all matrix entries via *, then * on A is given by \(x^*=c\bar x^ Tc^{-1}\) \((x\in A)\) for some ''\(\lambda\)-hermitian'' matrix C. A minor adjustment is needed in the general case.
scientific article; zbMATH DE number 4002303