Basic Notions, Ch III: Group Actions

Related lectures (31)

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Explores adjoint functors, points fixes, orbits, and non-trivial actions in group theory.

Covers proper actions of groups on Riemann surfaces and introduces algebraic curves via square roots.

Explores orbits in a G-ensemble, functions of fixed points, and G-equivariance.

Explores solvable groups, group actions, normalizers, and stabilizers in group theory.

Explores defining functors on morphisms, fixed points, orbits, equivariance, and composition preservation.

Covers fixed points, orbits, and stabilizers in G-varieties, including properties of closed subgroups and faithful actions.

Explores fixed points in G-sets, applications between sets, and the construction of orbits.

Explores adjunctions, emphasizing trivial and application quotient cases in functors, orbits, and fixed points.

Covers the introduction to Quantum Chaos, classical chaos, sensitivity to initial conditions, ergodicity, and Lyapunov exponents.

Covers the class equation in group theory and Burnside's Lemma, relating orbits and fixed points.