Further Directions: Algebraic Groups

Related lectures (29)

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Covers the structure of finite dimensional algebras and the characterization of semisimple algebras.

Covers the definitions and basic results of endomorphisms and automorphisms of totally disconnected locally compact groups.

Explores automorphism groups of trees and graphs, including actions on trees and group homomorphisms.

Introduces Lie algebras, vector spaces with a special bracket operation.

Explores the differential of group actions on vector spaces and the behavior of orbit maps.

Explores automorphisms of projective varieties, discussing isomorphism between complements and key observations on dimensions and examples.

Explores algebraic structures of morphism spaces, including stability properties and injective ring homomorphisms.

Covers examples of group algebra decomposition and simple infinite-dimensional algebras.

Explores Albanese varieties, Fourier-Mukai transforms, and positive characteristic applications.

Explores automorphisms of graphs, focusing on automorphism groups, Cayley-Abels graphs, and quasi-isometry.