Generators and Relations of the Affine Coordinate Rings of Connected Semisimple Algebraic Groups
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چکیده
Let G be a connected semisimple algebraic group over an algebraically closed field of characteristic zero. A canonical presentation by generators and relations of the algebra of regular functions on G is found. The conjectures of D.Flath and J.Towber, [FT], are proved. (1) Let G be a connected semisimple algebraic group over an algebraically closed field k of characteristic zero. We obtain here a canonical presentation of the algebra k[G] of regular functions on G (i.e., the affine coordinate ring of G) by means of generators and relations. In the simplest case when G = SL2 one has the isomorphism μ : k[A,B,C,D]/(AD −BC − 1) −→ k[G], (1.1)
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تاریخ انتشار 2000