Borel-Tits theorem

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Statement

Let G be a simple algebraic group over an algebraically closed field K, and H be a simple algebraic group over an algebraically closed field L. Let s be an isomorphism of groups between G and H (viz, only an isomorphism of the pure group structure). Then s can be decomposed into a transfer of structures induced by an isomorphism between K and L, followed by a quasi-rational function relative to L.

References

  • Homomorphismes abstraites de groupes algebriques simples by Armand Borel and J Tits, Ann. Math 97 (1973), 499-571