linear algebraic group
C44535
concept
A linear algebraic group is a group that is also an affine algebraic variety, whose group operations (multiplication and inversion) are given by regular polynomial maps when the group is realized as a closed subgroup of some general linear group GLₙ.
Observed surface forms (4)
- algebraic group ×1
- algebraic group constructions ×1
- linear algebraic groups ×1
- orthogonal group ×1
Instances (9)
- orthogonal group O(n)
- Chevalley groups via concept surface "linear algebraic groups"
- orthogonal group O(n+1,2) via concept surface "orthogonal group"
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special linear group SL(n,R)
surface form: SL(n,ℝ)
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general linear group GL(n,C)
surface form: GL(n,ℂ)
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special linear group SL(n,C)
surface form: SL(n,ℂ)
- SL(2,R)
- Langlands dual group via concept surface "algebraic group"
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PSL(2,\mathbb{C})
surface form: PSL(2,ℂ)