Decomposition of Group Algebras

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Subrepresentations of the regular representation

Explores subrepresentations of the regular representation in group theory, emphasizing properties and isomorphism between subrepresentations.

Algebraic Structures of Morphism Spaces

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

Linearly reductive groups

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

Rings and Modules: Color Codes and Homological Algebra

Covers rings and modules, emphasizing color codes and homological algebra concepts.

Algebraic Structures: Modules and Morphisms

Explores modules, sub-modules, and morphisms in algebraic structures.

Polynomials: Definitions and Operations

Covers the definition and operations of polynomials, including addition and multiplication, degree, coefficients, and their role in algebraic systems.

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Linear Algebra: Modules and Endomorphisms

Explores modules, endomorphisms, and linear applications in algebra, including A-modules and commutative rings.

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.

Coulomb Gas and Spin Chain: Quantum Group Applications

Explores the relationship between Coulomb gas models and spin chains in quantum groups.