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Lie Subgroups of the 2D Torus Group
Lie Subgroups of the 2D Torus Group
This Demonstration draws the one-dimensional Lie group plotted as a subgroup embedded (or immersed) in the two-dimensional torus group ={(exp(iθ),exp(iθ))|θ∈}. The slope is set by the direction of the velocity, and the subgroup is plotted from up to a maximum value set by the "length" value; this latter is the product of the "multiplier" value and the length of the velocity, so you can watch the thread grow by putting the velocity near (left-bottom corner) and dragging it to longer and longer lengths.
(α)={(exp(iθ),exp(iαθ))|θ∈}
2
α
θ=0
(0,0)