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algebraic group

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  • Algebraic group — In algebraic geometry, an algebraic group (or group variety) is a group that is an algebraic variety, such that the multiplication and inverse are given by regular functions on the variety. In category theoretic terms, an algebraic group is a… …   Wikipedia

  • Algebraic-group factorisation algorithm — Algebraic group factorisation algorithms are algorithms for factoring an integer N by working in an algebraic group defined modulo N whose group structure is the direct sum of the reduced groups obtained by performing the equations defining the… …   Wikipedia

  • Linear algebraic group — In mathematics, a linear algebraic group is a subgroup of the group of invertible n times; n matrices (under matrix multiplication) that is defined by polynomial equations. An example is the orthogonal group, defined by the relation MTM = I where …   Wikipedia

  • Adelic algebraic group — In mathematics, an adelic algebraic group is a topological group defined by an algebraic group G over a number field K , and the adele ring A = A ( K ) of K . It consists of the points of G having values in A ; the definition of the appropriate… …   Wikipedia

  • Semisimple algebraic group — In mathematics, especially in the areas of abstract algebra and algebraic geometry studying linear algebraic groups, a semisimple algebraic group is a type of matrix group which behaves much like a semisimple Lie algebra or semisimple ring.… …   Wikipedia

  • Differential algebraic group — In mathematics, a differential algebraic group is a differential algebraic variety with a compatible group structure. Differential algebraic groups were introduced by Cassidy (1972). References Cassidy, Phyllis Joan (1972), Differential algebraic …   Wikipedia

  • Radical of an algebraic group — In mathematics, an algebraic group G contains a unique maximal normal solvable subgroup; and this subgroup is closed. Its identity component is called the radical of G . External links * [http://eom.springer.de/R/r077110.htm Radical of a group ] …   Wikipedia

  • Group theory — is a mathematical discipline, the part of abstract algebra that studies the algebraic structures known as groups. The development of group theory sprang from three main sources: number theory, theory of algebraic equations, and geometry. The… …   Wikipedia

  • Algebraic — may refer to:* Algebraic chess notation mdash; a method used to record and describe the play of chess games. * Algebraic data types. * Algebraic group mdash; a term from algebraic geometry. * Algebraic numbers (those which are roots of certain… …   Wikipedia

  • Algebraic torus — In mathematics, an algebraic torus is a type of commutative affine algebraic group. These groups were named by analogy with the theory of tori in Lie group theory (see maximal torus). The theory of tori is in some sense opposite to that of… …   Wikipedia

  • Group of Lie type — In mathematics, a group of Lie type G(k) is a (not necessarily finite) group of rational points of a reductive linear algebraic group G with values in the field k. Finite groups of Lie type form the bulk of nonabelian finite simple groups.… …   Wikipedia

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