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Abelian space

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  • Abelian — Abelian, in mathematics, is used in many different definitions, named after Norwegian mathematician Niels Henrik Abel:In group theory:*Abelian group, a group in which the binary operation is commutative **Category of abelian groups Ab has abelian …   Wikipedia

  • Abelian von Neumann algebra — In functional analysis, an Abelian von Neumann algebra is a von Neumann algebra of operators on a Hilbert space in which all elements commute. The prototypical example of an abelian von Neumann algebra is the algebra L^infty(X,mu) for μ a σ… …   Wikipedia

  • Abelian variety — In mathematics, particularly in algebraic geometry, complex analysis and number theory, an Abelian variety is a projective algebraic variety that is at the same time an algebraic group, i.e., has a group law that can be defined by regular… …   Wikipedia

  • Abelian category — In mathematics, an abelian category is a category in which morphisms and objects can be added and in which kernels and cokernels exist and have desirable properties. The motivating prototype example of an abelian category is the category of… …   Wikipedia

  • Abelian group — For other uses, see Abelian (disambiguation). Abelian group is also an archaic name for the symplectic group Concepts in group theory category of groups subgroups, normal subgroups group homomorphisms, kernel, image, quotient direct product,… …   Wikipedia

  • Space group — In mathematics and geometry, a space group is a symmetry group, usually for three dimensions, that divides space into discrete repeatable domains. In three dimensions, there are 219 unique types, or counted as 230 if chiral copies are considered… …   Wikipedia

  • Abelian extension — In abstract algebra, an abelian extension is a Galois extension whose Galois group is abelian. When the Galois group is a cyclic group, we have a cyclic extension. More generally, a Galois extension is called solvable if its Galois group is… …   Wikipedia

  • Abelian variety of CM-type — In mathematics, an abelian variety A defined over a field K is said to have CM type if it has a large enough commutative subring in its endomorphism ring End(A). The terminology here is from complex multiplication theory, which was developed for… …   Wikipedia

  • Abelian and tauberian theorems — In mathematics, abelian and tauberian theorems relate to the meaningful assignment of a value as the sum of a class of divergent series. A large number of methods have been proposed for the summation of such series, generally taking the form of… …   Wikipedia

  • Rank of an abelian group — In mathematics, the rank, or torsion free rank, of an abelian group measures how large a group is in terms of how large a vector space over the rational numbers one would need to contain it; or alternatively how large a free abelian group it can… …   Wikipedia

  • Vector space — This article is about linear (vector) spaces. For the structure in incidence geometry, see Linear space (geometry). Vector addition and scalar multiplication: a vector v (blue) is added to another vector w (red, upper illustration). Below, w is… …   Wikipedia

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