On conjugacy classes of maximal tori in classical groups (Q1824035)

Let K be an infinite field and SL, Sp, SO are classical algebraic groups defined over K. In the paper a complete classification of the K-conjugacy classes of maximal K-tori in these groups is given. Let G be such a classical group, for each K-conjugacy class of maximal K-tori of G, a K- isomorphism class of commutative semi-simple K-algebras with involutions is naturally obtained and the image of this correspondence is determined. Furthermore for each K-isomorphism class of such K-algebras in its image, the cardinality of all conjugacy classes of maximal K-tori of G corresponding to it is calculated.