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Dimension as varieties

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Joubert

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Jul 6, 2009, 2:02:48 PM7/6/09
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Whats the dimension of O(n,K) (the orthogonal group) as an algebraic group?

Mariano Suárez-Alvarez

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Jul 6, 2009, 3:10:05 PM7/6/09
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On Jul 6, 3:02 pm, Joubert <theawesomo408...@yahoo.com> wrote:
> Whats the dimension of O(n,K) (the orthogonal group) as an algebraic group?

O(n,K) is, naively, the set of n-by-n matrices X such that
transpose(X) . X = Id. Differentiate this condition to
obtain linear equations for the Lie algebra, and then compute
the dimension of the Lie algebra.

-- m

Joubert

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Jul 7, 2009, 12:29:56 PM7/7/09
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Mariano Su�rez-Alvarez wrote:

> O(n,K) is, naively, the set of n-by-n matrices X such that
> transpose(X) . X = Id. Differentiate this condition to
> obtain linear equations for the Lie algebra, and then compute
> the dimension of the Lie algebra.

Thnaks

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