How to Construct Every Symmetry | Decomposition, Extension, and Classification of Groups скачать в хорошем качестве

How to Construct Every Symmetry | Decomposition, Extension, and Classification of Groups

Group is a mathematical abstraction used to describe symmetry. In this video, we introduce the theory of groups, group decomposition and extension, and computational aspects as to why classifying all finite groups is impossible. Links: Video that introduces sporadic groups Why Do Sporadic Groups Exist?:    • Why Do Sporadic Groups Exist?   Video that explains both algebraic and topological aspect of the spin group Dirac's belt trick, Topology, and Spin ½ particles:    • Dirac's belt trick, Topology,  and Spin ½ ...   Video for understanding the geometry of unit quaternions Visualizing quaternions (4d numbers) with stereographic projection:    • Visualizing the 4d numbers Quaternions   Video that constructs the spin group as SU(2) axiomatically The biggest misconception about spin 1/2:    • The biggest misconception about spin 1/2   Entire video series on spinors Spinors for Beginners:    • Spinors for Beginners   Eilenberg and Maclane's original paper on group extensions with non-Abelian normal subgroup Group Extensions with a non-Abelian Kernel: https://shorturl.at/ryFLZ And here are some resources to learn more about group extension: ncatlab: https://ncatlab.org/nlab/show/group+e... groupprops: https://groupprops.subwiki.org/wiki/G... Chapters: 00:00 Intro 01:21 Examples of Groups 02:50 Equivalent Groups 05:32 Abstract Definition of a Group 07:22 Definition of Isomorphism 08:24 Automorphism Group 10:28 Decomposition of Groups 14:48 Finite Simple Groups 17:07 Infinite Group Cannot Be Factored 18:33 Group Extension 19:18 Direct Product / Classification of Abelian Groups 24:14 Semidirect Product 26:51 Non-split Extensions 31:45 What is Cohomology 35:37 Why Classification of Groups is So Hard 36:32 Isomorphism Testing Algorithm 39:02 Status on Classification of Groups 39:46 Classification of Groups of Order 16 42:42 Asymptotic Group Theory 43:32 Chemistry Analogy 44:45 Outro Music🎵: No.3 Morning Folk Song – Esther Abrami    • No.3 Morning Folk Song   Corrections: 0:37 60 = 2 × 2 × 3 × 5