The J Function, SL(2) and the Jacobi Identity - Universal Hyperbolic Geometry
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This course connects hyperbolic points and matrices through the J function and the sl(2) Lie algebra. It uses the Jacobi identity to give a projective proof of the concurrence of a triangle’s altitudes and the existence of its orthocenter.
Syllabus
Introduction, the J function, sl2, the Jacobi identity
sl2 Lie algebra
Jacobi identity
Projective algebra of matrices
Projective parametrization of null circle
General formula for reflection
The meaning of the Jacobi identity
Taught by
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