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Related lectures (15)

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The Torus and Linear Groups

Explores the torus, linear groups, stability properties of matrices, and homomorphisms.

Linear Projective Groups

Explores linear projective groups, quaternions, subgroup generation, and normality.

Self-similar groups II

Explores self-similar groups acting on rooted trees and their properties.

Covers self-similar groups and automorphisms of rooted trees, exploring residually finite groups and congruence subgroups.

Dynamics on Homogeneous Spaces and Interactions with Number Theory

Explores dynamics on homogeneous spaces and their interactions with number theory, focusing on modular lattices and the Iwasawa decomposition theorem.

Matrix Operations: Scaling and Invertibility

Covers scaled matrices, ladder matrices, and the Gauss method for matrix operations.

Symplectic Groups

Explores symplectic groups, linear transformations preserving non-degenerate alternating bilinear forms on vector spaces.

Group Actions: Examples

Showcases examples of group actions on vector spaces and topological spaces.

Linear algebraic groups

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

Subrepresentations of the regular representation

Explores subrepresentations of the regular representation in group theory, emphasizing properties and isomorphism between subrepresentations.