Abelian
# Abelian

Abelian may refer to:

## Mathematics

### 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

### 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

### Other mathematics

* Abelian category, in category theory, a preabelian category in which every monomorphism is a kernel and every epimorphism is a cokernel
* Abelian and Tauberian theorems, in real analysis, used in the summation of divergent series
* Abelian extension, in Galois theory, a field extension for which the associated Galois group is abelian
* Abelian von Neumann algebra, in functional analysis, a von Neumann algebra of operators on a Hilbert space in which all elements commute

## Other uses

* Abelian, in physics, a gauge theory with a commutative symmetry group
* Hovhannes Abelian (1865–1936), Armenian actor
