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Related lectures (52)

Symmetries and Groups in Quantum Mechanics

Covers the role of symmetries and groups in quantum mechanics, focusing on SU2 and SU3, their properties, and implications for physical theories.

Automorphism Groups: Trees and Graphs III

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

Local Homeomorphisms and Coverings

Covers the concepts of local homeomorphisms and coverings in manifolds, emphasizing the conditions under which a map is considered a local homeomorphism or a covering.

Group Theory Basics: Subgroups and Homomorphisms

Introduces subgroups and homomorphisms in group theory, with examples for illustration.

Endomorphisms and automorphisms of totally disconnected locally compact groups I

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

Diagonalizable Groups Log in to Mediaspace to watch this video

Explores the concept of diagonalizable groups and their properties in linear algebraic groups.

Commutative algebraic groups Log in to Mediaspace to watch this video

Covers the properties of commutative linear algebraic groups and their elements.

Subgroups and subalgebras Log in to Mediaspace to watch this video

Explores the unique determination of homomorphisms by differentials and the intersection of closed subgroups' Lie algebras.

Jordan decomposition: Lie algebra Log in to Mediaspace to watch this video

Delves into the Jordan decomposition in Lie algebras of linear algebraic groups.

Quotients of Linear Groups by Linearly Reductive Groups Log in to Mediaspace to watch this video

Explores constructing quotients of linear algebraic groups by linearly reductive sub-groups.

Subgroups and Cosets: Lagrange's Theorem Log in to Mediaspace to watch this video

Explores subgroups, normal subgroups, cosets, and Lagrange's theorem in group theory, emphasizing the importance of left cosets.

Dihedral Group: Symmetries and Cosets Log in to Mediaspace to watch this video

Explores the symmetries of a regular n-gon, normal subgroups, cosets, and Lagrange's theorem.

Linear algebraic groups Log in to Mediaspace to watch this video

Covers linear algebraic groups, including special sets and matrix examples.

Lagrange's Theorem: Applications and Homomorphisms Log in to Mediaspace to watch this video

Covers Lagrange's theorem, group homomorphisms, congruence classes, and normal subgroups.

Permutations and Adjacency Log in to Mediaspace to watch this video

Explores permutations preserving adjacency, linear transformations, groups, and sub-groups.

Untitled Log in to Mediaspace to watch this video

Mathematical Parenthesis on Groups and Lagrange Theorem Log in to Mediaspace to watch this video

Explores cosets in commutative groups, Lagrange theorem, and integer factorization.

Characters: Linear Algebraic Groups Log in to Mediaspace to watch this video

Introduces characters as group homomorphisms from linear algebraic groups to multiplicative groups.

Group Homomorphisms: Kernels, Images, and Normal Subgroups Log in to Mediaspace to watch this video

Explores group homomorphisms, kernels, images, and normal subgroups, using the dihedral group D_n as an example.

Group Theory: Quotients of Group Log in to Mediaspace to watch this video

Covers normal subgroups, quotient groups, homomorphisms, and the categorical viewpoint in group theory.

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