Monday, 11 June 2012

ag.algebraic geometry - Subgroup Groups and Coordinate Algebra Subalgebras

It may be possible in rare circumstances, but the natural thing is that mathcalO(H) is a quotient of mathcalO(G), not a subalgebra. The quotient map is dual to the inclusion HtoG.



I guess in the case that G is a direct product HtimesK, you get
mathcalO(G)simeqmathcalO(H)otimesmathcalO(K),


and in this case you have what you want. But in general, the arrow should go the other direction.

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