On division algebras of degree 3 with involution
The authors present a simple proof of the theorem [\textit{A. A. Albert}, Scripta Math. 26, 309-316 (1963; Zbl 0147.28702)] that a division algebra of degree 3 (in characteristic not 3) with an involution \(J\) of the second kind has a maximal subfield which is Galois over the fixed field of \(J\), with the symmetric group of degree 3 as Galois group. The argument also provided another proof of Wedderburn's theorem that central division algebras of degree 3 are cyclic. The result is applied to prove that every central simple algebra of degree 3 with an involution of the second kind is a homomorphic image of the Clifford algebra of a binary cubic form with its canonical involution. For a given form this leads to a classification of these images.
scientific article; zbMATH DE number 941280