Lie Algebras and Representations

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Related lectures (42)

Ideals and Representations Log in to Mediaspace to watch this video

Covers ideals, representations, modules, and maximal ideals in associative algebras.

Complete Reducibility of Complex Representations Log in to Mediaspace to watch this video

Covers the complete reducibility of complex representations and the relation between Lie algebras and Lie groups.

Structure of Algebras Log in to Mediaspace to watch this video

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

Density Theorem: Endomorphisms of Simple Modules Log in to Mediaspace to watch this video

Covers the density theorem in representation theory, focusing on endomorphisms of simple finite-dimensional modules.

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

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

Machine Learning at the Atomic Scale Log in to Mediaspace to watch this video

Explores simple models, electronic structure evaluation, and machine learning at the atomic scale.

Weyl character formula Log in to Mediaspace to watch this video

Explores the proof of the Weyl character formula for finite-dimensional representations of semisimple Lie algebras.

Group Actions: Differential of Orbit Map Log in to Mediaspace to watch this video

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

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 and Symmetric Power Log in to Mediaspace to watch this video

Covers tensor products, symmetric power, and exterior power of vector spaces, including properties and applications.

Linear Algebra: Multilinear Forms Log in to Mediaspace to watch this video

Explores multilinear forms in linear algebra, emphasizing their properties and applications.

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

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

Decomposition Spectral: Symmetric Matrices Log in to Mediaspace to watch this video

Covers the decomposition of symmetric matrices into eigenvalues and eigenvectors.

Orthogonally Diagonalizable Matrices Log in to Mediaspace to watch this video

Explores orthogonally diagonalizable matrices, eigenvectors, bases, and matrix properties.

Orthogonal Diagonalization: Symmetric Matrices Log in to Mediaspace to watch this video

Explores orthogonal diagonalization for symmetric matrices in linear algebra.

Stress and Strain: Generalization to 3D Log in to Mediaspace to watch this video

Covers stress equilibrium, strain, and the generalization of stress to 3D, introducing Hooke's Law and analyzing structures with axial loads.

Stochastic Block Model: Community Detection Log in to Mediaspace to watch this video

Covers the Stochastic Block Model for community detection, focusing on the detection of communities, clusters, and groups.

Stabilizer Formalism: Kuill-Laflamme Theorem Log in to Mediaspace to watch this video

Covers the Kuill-Laflamme theorem and the stabilizer formalism for Quantum Error Correcting Codes.

Symmetries in Regular Polygons Log in to Mediaspace to watch this video

Delves into the symmetries of regular polygons, including the dihedral group and left cosets in a finite group.

Determinants: Alternate Forms and Symmetrization Log in to Mediaspace to watch this video

Explores alternate forms, symmetric forms, and determinants in linear algebra.

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