Concept

D-module

Related lectures (18)

Simple Modules: Schur's Lemma

Covers simple modules, endomorphisms, and Schur's lemma in module theory.

Algebraic Structures of Morphism Spaces

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

Decomposition of Group Algebras

Covers examples of group algebra decomposition and simple infinite-dimensional algebras.

Module Theory: Definitions and Examples

Introduces the definition and examples of A-modules, including sub-modules and ideals.

Modules of Covariants

Explores the decomposition of the circle of the coordinate ring of a G variety into a direct sum of simple submodules.

Injective Modules: Ox-Modules and Injectives

Covers injective modules, Ox-modules, and their relevance in algebraic structures, emphasizing their importance in resolving acyclic resolutions and computing cohomology.

Coherent Risk Measures: Spectral Approach

Explores coherent risk measures and the spectral approach to risk aversion, covering VaR, ES, subadditivity, convexity, and the creation of new risk measures.

Ideals and Representations

Covers ideals, representations, modules, and maximal ideals in associative algebras.

Data Abstraction: Modules and Specifications in Coq

Discusses data abstraction in programming, focusing on modules and specifications in Coq.

Module Theory: Chain Conditions

Explores chain conditions in module theory, emphasizing Noetherian modules and stabilizing sequences of submodules.

Weyl character formula

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

Adjunctions and Applications

Covers adjunctions, projective varieties, regularity, and valuative criteria in algebraic geometry.

Coherent Sheaves: Locally Ringed Space

Covers the definition of coherent sheaves and their properties in the context of algebraic geometry.

Geometric Objects in Algebra

Covers the study of graded modules and quasicoherent sheaves in algebraic geometry.

Vector Bundles & Locally Free Sheaves

Covers vector bundles, locally free sheaves, depth, Serre twisting sheaf, and graded modules in algebraic geometry.

Group Algebra: Maschke's Theorem

Explores Wedderburn's theorem, group algebras, and Maschke's theorem in the context of finite dimensional simple algebras and their endomorphisms.

Tensor Products of Modules

Covers tensor algebras, symmetric and exterior algebras, and tensor products of modules.

Genetic Circuits: Synthetic Biology

Covers genetic circuits in synthetic biology, including metabolic engineering, lac operon regulation, and synthetic circuit design.