Algebra: Fundamental TheoremCovers a general introduction and discusses algebra, emphasizing the importance of unique factorization in algebraic structures.
Discrete Valuation RingsExplores discrete valuation rings, their properties, uniqueness of representation, and relationship with principal ideal domains.
Lie Algebra: Group TheoryExplores Lie Algebra's connection to Group Theory through associative operations and Jacobi identities.
Group Algebra: Maschke's TheoremExplores Wedderburn's theorem, group algebras, and Maschke's theorem in the context of finite dimensional simple algebras and their endomorphisms.
Factorisation in PIDsCovers factorisation in PIDs, prime ideals, unique tuples, and common prime factors.
Macdonald identitiesDelves into Macdonald identities, covering affine root systems, modular forms, and Lie algebras.
Weyl character formulaExplores the proof of the Weyl character formula for finite-dimensional representations of semisimple Lie algebras.