Representation of Groups

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Related lectures (30)

Fundamental Groups

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

Group representations constructions

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

Lemma of Schur: Group Repetition Theory

Explores irreducible and reducible representations in group repetition theory and the lemma of Schur in quantum physics.

Molecular Orbital Theory

Covers the concept of eigenfunctions of H as bases for irreducible representations and integrals.

Lie Groups and Lorentz Transformations

Covers Lie groups, Lorentz transformations, boosts, rotations, and complexified Lie algebras.

Homomorphism of Groups: Signature

Explores homomorphisms of groups, focusing on the signature sgn and the concept of cycles and transpositions.

Categorical Perspective: Group Actions

Generalizes group actions beyond sets, providing a comprehensive framework for various mathematical contexts.

Decomposition of Group Algebras

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

Amalgams: Group Pushouts

Covers the concept of amalgams, defining pushouts and quotient groups in group theory.

Machine Learning at the Atomic Scale

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

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