#group
5 concepts
Concepts
Group Theory
A group is a set with a binary operation satisfying associativity, existence of identity, and existence of inverses. It's the fundamental structure for studying symmetry mathematically.
Lie Groups
Structure that is both a group and differentiable manifold. Describes continuous symmetries
Group Representation
Homomorphism realizing group as group of invertible linear transformations on vector space
Lie Group
A group with smooth manifold structure. Group operations are differentiable, representing continuous symmetries.
Fourier Analysis on Groups
Generalizes Fourier analysis to locally compact abelian groups. Pontryagin duality is the key theorem.