Group Theory

concepts · 11 notes linked

Related: Representation Theory · Harmonic Analysis · Linear Algebra · Abstract Algebra · Lie Groups · Lie Algebras · Hermann Weyl · Fritz Peter

Notes

• Compact group - Wikipedia — Topological groups with compact topology and their complete representation theory
• Conjugacy class - Wikipedia — Equivalence classes under group conjugation relation
• General linear group - Wikipedia — Group of invertible n-by-n matrices under multiplication
• Group Explorer 2.2 — Visual software tool for exploring finite group structures
• Groupprops, The Group Properties Wiki (beta) — Collaborative reference wiki for group theory properties
• Octahedral symmetry - Wikipedia — Symmetry group of the cube and octahedron with 48 total isometries
• Peter–Weyl theorem - Wikipedia — Harmonic analysis decomposition theorem for compact topological groups
• Representation theory - Wikipedia — Studying abstract algebra via linear transformations of vector spaces
• The 'Useless' Perspective That Transformed Mathematics — Representation theory maps abstract groups to concrete matrices
• What Are Lie Groups? | Quanta Magazine — Lie groups as continuous-symmetry manifolds bridging algebra, geometry, and physics
• Young tableau - Wikipedia — Combinatorial diagrams encoding symmetric and linear group representations