Lectures related to Finitely generated algebra

Explores isotypic decomposition in finitely generated C-algebras and its implications, including G-stable ideals and linear projections.

Covers rings, modules, exact sequences, and finitely generated modules in the context of Noetherian and Artinian properties.

Covers proper actions of groups on Riemann surfaces and introduces algebraic curves via square roots.

Covers the topology of Riemann surfaces and the concept of triangulation using finitely many triangles.

Introduces Noetherian modules and explores simple modules and composition series.

Explores flat groups of automorphisms and their properties, including minimization functions and invariance under specific conditions.

Covers the concept of algebraic quotients in the context of a-variety.

Explores self-similar groups acting on rooted trees and their properties.

Covers the fundamental theorem of finitely generated modules over a PID.

Explores the additivity of dimension and height in a finitely generated k-algebra domain, showcasing its applications and implications.

Explores module generation, submodules, modulus, finite type modules, and morphisms.

Explores transfer operators, Patterson-Sullivan measure, FUP, spectral gaps, and resonances in Schottky groups.

Explores Dedekind rings, integral extensions, and noetherian rings in algebraic structures.

Explores ramification theory, residual fields, and discriminant ideals in algebraic number theory.

Covers 3D orientation, cross product, and volume calculations using mixed product in vector calculus.

Covers the structure of finite dimensional algebras and the characterization of semisimple algebras.

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

Covers the recap of Galois theory and emphasizes the transitivity of Galois groups.

Explores ramification and structure of finite extensions of Qp, including unramified extensions and Galois properties.