Geodesic
Algebraic transformation groups of maximal rank
Sbornik. Mathematics, Tome 17 (1972) no. 4, pp. 487-496

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We give a birational classification of all connected algebraic transformation groups whose reductive rank equals the dimension of the variety being acted upon. Bibliography: 1 title. 
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     author = {\`E. B. Vinberg},
     title = {Algebraic transformation groups of maximal rank},
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È. B. Vinberg. Algebraic transformation groups of maximal rank. Sbornik. Mathematics, Tome 17 (1972) no. 4, pp. 487-496. http://geodesic.mathdoc.fr/item/SM_1972_17_4_a1/