Group Algebra: Maschke's Theorem

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Discusses linearly reductive groups and their properties, focusing on completely reducible representations and equivalent modules.

Lie Groups: Representations and Transformations

Explores Lie groups, scalar fields, and vector spaces transformations.

Dimension Theory of Rings

Explores the dimension theory of rings, focusing on chains of ideals and prime ideals.

Fundamental Groups

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

Lie Algebras: Introduction and Structure

Introduces Lie algebras, vector spaces with a special bracket operation.

Finite Abelian Groups: Classification Theorem

Presents the classification of finite abelian groups as products of cyclic groups, a fundamental result in various branches of mathematics.

Completely Reducible Representations

Covers completely reducible representations, simple modules, semisimple modules, and G-stable submodules.

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.

Algebraic Structures of Morphism Spaces

Explores algebraic structures of morphism spaces, including stability properties and injective ring homomorphisms.