Modules of Covariants

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Related lectures (31)

Page 3 of 4

The Regular Representation

Introduces the regular representation, a key tool for studying group actions on varieties.

Linear Representations: Basics and Examples

Covers linear representations, isomorphism, G modules, and classification of representations of C star and C plus.

Connected groups of semisimple elements

Explores weight space decomposition and proves that a connected linear algebraic group with all semi-simple elements must be a torus.

Weyl character formula

Explores the proof of the Weyl character formula for finite-dimensional representations of semisimple Lie algebras.

Module Theory: Noetherian Modules

Introduces Noetherian modules and explores simple modules and composition series.

Polynomials: Definitions and Operations

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

Cohomology: Cross Product

Explores cohomology and the cross product, demonstrating its application in group actions like conjugation.

Algebraic Structures: Modules and Morphisms

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

Algebraic Geometry: Localization and Prime Ideals

Explores prime ideals and localization in algebraic geometry, highlighting their significance in ring structures.

Linear Algebra: Modules and Endomorphisms

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