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)