Associative rings and algebras Hopf algebras and quantum groups Concept
Hopf algebra
Summary
A Hopf algebra is a bialgebra with an antipode, a linear map that plays the role of taking inverses in a group. Group algebras, coordinate rings of affine algebraic groups and universal enveloping algebras of Lie algebras are the main classical examples. Quantum groups are Hopf algebras that deform these examples. Hopf algebras also appear in algebraic topology, as the cohomology of Lie groups and H-spaces, and in combinatorics and renormalization.
Where this leads
11 pages build on this one.
Further reading
About this page
| Tag | 7XFYP0N84H |
|---|---|
| URI | m2://7XFYP0N84H |
| Kind | concept |
| Writing | W0 stub |
| MSC | 16T05 |
| Specializes | Bialgebra |
| Same as |
Markdown · JSON · Edit on GitHub
What this page needs for W1
- a source with a locator (0 of 1)
The writing levels say how complete the text of a page is. They do not measure its truth.
What links here
Used by
- Integral of a Hopf algebra
- Quasitriangular Hopf algebra
- Hopf module
- Ribbon Hopf algebra
- Butcher group
- Nichols–Zoeller theorem
- Larson–Sweedler theorem
- Cartier–Milnor–Moore theorem
- Smash product
- Quantum group
- Quantum enveloping algebra