Concept

Group extension

Related lectures (31)

Classification of Extensions

Explores the classification of extensions in group theory, emphasizing split extensions and semi-direct products.

Approximation in Sobolev Spaces

Covers the approximation of functions in Sobolev spaces using smooth functions.

Properties of Finite Dimensional Algebras

Covers the properties of finite dimensional algebras and non-semisimple representations.

Galois Theory: Recap and Transitivity

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

Damped Harmonic Oscillator

Covers the damped harmonic oscillator in quantum optics, discussing alternative descriptions and extensions like finite temperature.

Torsion and Divisibility in Group Theory

Explores the relationship between p-torsion and p-divisibility in group theory, highlighting implications of p-divisibility in exact sequences of abelian groups.

Extension of Fields: Norm and Valuation

Covers the extension of fields, defining the norm of an element from one field to another, and introducing the p-adic valuation.

Stochastic Integral: Isometry Continuity

Covers stochastic integrals, emphasizing isometry and continuity properties in martingales and different spaces.

Topology: Lecture Notes 2021

Covers commutative diagrams, homotopy, and constructing topological spaces.

Heisenberg Group: Representation

Covers the Heisenberg group representation, including shifts, multiplications, and the Fourier transform, extending to finite fields and metaplectic groups.

Polymerase Chain Reaction: Basics and Process

Explains the basics and process of Polymerase Chain Reaction (PCR) and the collaboration behind the content.

Multiple Integrals: Extension and Properties

Explores the extension and properties of multiple integrals for continuous functions on rectangles.

Matroids: Matroid Intersection

Covers the concept of matroids, focusing on matroid intersection and the properties of subsets of a ground set.

Algebraic Extensions and Decomposition of Fok [x]

Covers homomorphisms, algebraic extensions, cutting, splitting, and separable elements in Fok [x].

Manifolds: Charts and Compatibility

Covers manifolds, charts, compatibility, and submanifolds with smooth analytic equations.

Infinity Category Theory: Extensions and Equivalences

Explores right extensions in infinity category theory and their equivalent definitions.

Special open sets and epsilonization

Covers the concept of special open sets and epsilonization, discussing unique extensions of derivations and specific value settings.

Algebraic Extensions

Explores algebraic extensions, constructions, irreducible polynomials, autonomous constructions, and cutting compositions.

Limits and Continuity

Covers limits, continuity, and the intermediate value theorem in functions.

Mathematical Analysis: Functions and Composition

Covers the analysis of functions, composition, and mathematical induction.