Hopf algebra (concept named after him)

E679321

A Hopf algebra is an abstract algebraic structure that unifies and generalizes groups, rings, and vector spaces, playing a central role in areas such as algebraic topology, quantum groups, and category theory.

All labels observed (2)

Label Occurrences
Hopf algebra 3
Hopf algebra (concept named after him) canonical 1

How this entity was disambiguated

Statements (54)

Predicate Object
instanceOf algebraic structure
mathematical concept
appearsIn algebraic K-theory
linked to: Quillen K-theory

stable homotopy theory
condition antipode is convolution inverse of identity
comultiplication is an algebra homomorphism
counit is an algebra homomorphism
definedOver commutative ring
field
example Connes–Kreimer Hopf algebra
Hopf algebra of symmetric functions
Sweedler’s 4-dimensional Hopf algebra
coordinate ring of an algebraic group
group algebra of a group
quantum enveloping algebra U_q(g)
universal enveloping algebra of a Lie algebra
field abstract algebra
algebraic topology
category theory
noncommutative geometry
quantum algebra
representation theory
generalizes Lie algebra (via universal enveloping algebra)
linked to: Lie algebras

bialgebra
coalgebra
group
group algebra
ring
hasPart algebra structure
antipode
coalgebra structure
comultiplication
counit
multiplication
unit
namedAfter Heinz Hopf
property algebra and coalgebra structures are compatible
antipode is anticomultiplicative
antipode is antimultiplicative
comultiplication is coassociative
counit satisfies counit axioms
simultaneously an algebra and a coalgebra
relatedConcept Tannaka–Krein duality
bialgebra
monoidal category
quantum group
usedIn Hopf–Galois theory
algebraic topology
combinatorics
deformation quantization
homotopy theory
knot invariants
quantum groups
topological quantum field theory

How these facts were elicited

Referenced by (4)

Full triples — surface form annotated when it differs from this entity's canonical label.

Heinz Hopf notableWork Hopf algebra (concept named after him)
Heinz Hopf notableFor Hopf algebra
subject linked to: Hopf
linked to: Hopf algebra (concept named after him)
Hopf hasNotableMathematicalConceptNamedAfter Hopf algebra
linked to: Hopf algebra (concept named after him)
Heinz Hopf notableFor Hopf algebra
subject linked to: Gräbschen
linked to: Hopf algebra (concept named after him)