Geodesic
Representation of Algebras with Involution
Canadian journal of mathematics, Tome 24 (1972) no. 4, pp. 592-597

Voir la notice de l'article provenant de la source Cambridge University Press

Let K be a field with an involution J. A *-algebra over K is an associative algebra A with an involution * satisfying (α.a)* = αJ.a*. A large class of examples may be obtained as follows. Let (V, φ) be an hermitian space over K consisting of a vector space V and a left hermitian (w.r.t. J) form φ on V which is nondegenerate in the sense that φ(V,v) = 0 implies v = 0. An endomorphism f of V may have an adjoint f * w.r.t. φ, defined by φ(f(u),v) = φ(u,f*(v)); due to the nondegeneracy of φ, f* is unique if it exists. The set B(V, φ) of all endomorphisms of V which do have an adjoint is easily verified to be a *-algebra. 
Maxwell, George. Representation of Algebras with Involution. Canadian journal of mathematics, Tome 24 (1972) no. 4, pp. 592-597. doi: 10.4153/CJM-1972-053-4
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