Lectures related to Relations and Subsystems

Covers the goals and motivations of representation theory, focusing on associative algebras and homomorphisms.

Explores representations of C3v symmetry, character tables, Mulliken symbols, and group theory applications in eigenfunctions.

Explores character representations in group repetition theory, discussing irreducibility, equivalence, and associated values.

Explores chirality, group completeness, Abelian groups, conjugate classes, and isomorphic groups in symmetry and group theory.

Explores representation theory and character theory of finite groups, including scalar product and McKay graph.

Explores group representations using matrices, discussing reducible vs. irreducible representations and the Great Orthogonality Theorem.

Explores Lie algebras, representations, tensor products, and commutation relations in mathematics.

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

Explores group theory in quantum physics, emphasizing reducible and irreducible representations, conservation laws, and group properties.

Explores k-fold degenerate sets of eigenfunctions and their basis for irreducible representations.

Explores irreducible representations of the rotations group and their mathematical properties.

Covers topics related to quantum chemistry, including observable operators and eigenvalues.

Explains the tensor product of representations in quantum physics and the properties of defined actions.

Covers the application of group representations theory in quantum physics.

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

Covers the representation theory of groups, focusing on actions and invariants.

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

Explores Poincaré irreducible representations, Little Group, and induced representation in the context of momentum eigenstates.

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

Explores the construction of matrices representing group representations and the importance of symmetry in characterizing physical phenomena.