Abelian
In mathematics, abelian refers to any of a number of different mathematical concepts named after Niels Henrik Abel:
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Look up Abelian or abelian in Wiktionary, the free dictionary. |
Group theory
- Abelian group, a group in which the binary operation is commutative
- Category of abelian groups Ab has abelian groups as objects and group homomorphisms as morphisms
- Metabelian group, a group where the commutator subgroup is abelian
- Abelianisation
Galois theory
- Abelian extension, a field extension for which the associated Galois group is abelian
Real analysis
- Abelian and tauberian theorems, used in the summation of divergent series
Functional analysis
- Abelian von Neumann algebra, a von Neumann algebra of operators on a Hilbert space in which all elements commute
Topology and number theory
- Abelian variety, a complex torus that can be embedded into projective space
- Abelian surface, a two-dimensional abelian variety
- Abelian function, a meromorphic function on an abelian variety
- Abelian integral, a function related to the indefinite integral of a differential of the first kind
Category theory
- Pre-abelian category, an additive category that has all kernels and cokernels
- Abelian category, a preabelian category in which every monomorphism is a kernel and every epimorphism is a cokernel
Physics
- A gauge theory is abelian or non-abelian depending on whether its symmetry group is commutative or non-commutative, respectively
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