The classical Lie algebras

Related lectures (32)

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Explores the properties of Euclidean domains, including gcd, lcm, and the Chinese remainder theorem for polynomial rings.

Explores the construction and properties of finite fields, including irreducible polynomials and the Chinese Remainder Theorem.

Explores Lie algebra, Casimirs, and Poincaré in SO(3) transformations.

Covers factorisation in PIDs, prime ideals, unique tuples, and common prime factors.

Covers principal ideals, ring homomorphisms, and more in commutative rings and fields.

Explores Einsteinian relativity, the Lorentz group, and Poincaré transformations, emphasizing proper and non-orthochronous components.

Covers Lie algebra, group representations, symmetry groups, and Schur's lemma in the context of symmetry and group operations.

Delves into Macdonald identities, covering affine root systems, modular forms, and Lie algebras.

Covers the properties of the ring of Eisenstein integers and its submodule structure.

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