Completely Reducible Representations

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Module Theory: Noetherian Modules Log in to Mediaspace to watch this video

Introduces Noetherian modules and explores simple modules and composition series.

Module Theory: Chain Conditions Log in to Mediaspace to watch this video

Explores chain conditions in module theory, emphasizing Noetherian modules and stabilizing sequences of submodules.

Schur's Lemma and Representations Log in to Mediaspace to watch this video

Explores Schur's lemma and its applications in representations of an associative algebra over an algebraically closed field.

Kirillov Paradigm for Heisenberg Group Log in to Mediaspace to watch this video

Explores the Kirillov paradigm for the Heisenberg group and unitary representations.

G-modules and G-varieties Log in to Mediaspace to watch this video

Explores the embedding of chi-varieties into vector spaces with linear actions.

Group representations constructions Log in to Mediaspace to watch this video

Explores the construction of group representations through various methods and provides an illustrative example using the standard representation of sr2 on c2.

Tensor Products of Modules Log in to Mediaspace to watch this video

Covers tensor algebras, symmetric and exterior algebras, and tensor products of modules.

Free Resolution of Modules Log in to Mediaspace to watch this video

Covers free resolution of modules and projective modules in module theory.

Rings and Modules: Lecture 1 Log in to Mediaspace to watch this video

Covers rings, modules, exact sequences, and finitely generated modules in the context of Noetherian and Artinian properties.

Connected groups of semisimple elements Log in to Mediaspace to watch this video

Explores weight space decomposition and proves that a connected linear algebraic group with all semi-simple elements must be a torus.

Monster Group: Representation Log in to Mediaspace to watch this video

Explores the Monster group, a sporadic simple group with a unique representation theory.

System Composition Log in to Mediaspace to watch this video

Covers system composition, feedback representation, and block diagrams of LTI systems.

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