Abelian

Abelian may refer to:

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