Lecture
Group Actions: Differential of Orbit Map
Related lectures (44)
Representation Theory: Algebras and Homomorphisms
Covers the goals and motivations of representation theory, focusing on associative algebras and homomorphisms.
The Regular Representation
Introduces the regular representation, a key tool for studying group actions on varieties.
Kirillov Paradigm for Heisenberg Group
Explores the Kirillov paradigm for the Heisenberg group and unitary representations.
Group Algebra: Maschke's Theorem
Explores Wedderburn's theorem, group algebras, and Maschke's theorem in the context of finite dimensional simple algebras and their endomorphisms.
Lie Algebras: Introduction and Structure
Introduces Lie algebras, vector spaces with a special bracket operation.
Connected groups of semisimple elements
Explores weight space decomposition and proves that a connected linear algebraic group with all semi-simple elements must be a torus.
Lie Algebras and Representations
Explores Lie algebras, representations, tensor products, and commutation relations in mathematics.
Lie Groups: Representations and Transformations
Explores Lie groups, scalar fields, and vector spaces transformations.
Lie Algebra: Representations and Symmetry Groups
Covers Lie algebra, group representations, symmetry groups, and Schur's lemma in the context of symmetry and group operations.
Weyl character formula
Explores the proof of the Weyl character formula for finite-dimensional representations of semisimple Lie algebras.