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The J Function, SL(2) and the Jacobi Identity - Universal Hyperbolic Geometry

Insights into Mathematics via YouTube

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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

Insights into Mathematics

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