Properties of Finite Dimensional Algebras

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Page 3 of 4

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

Completely Reducible Representations

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

Affine Algebraic Sets

Covers affine algebraic sets, hypersurfaces, elliptic curves, ideals, and Noetherian rings in algebraic geometry.

Subrepresentations of the regular representation

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

Algebraic Structures: Modules and Morphisms

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

Separable Extensions: Dedekind Rings

Explores separable extensions and Dedekind rings, focusing on coefficients and prime ideals.

Lie Algebras and Representations

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

Polynomials: Definitions and Operations

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

Complete Reducibility of Complex Representations

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

Rings and Modules: Color Codes and Homological Algebra

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