irreducible module

irreducible module
мат.
неприводимый модуль

English-Russian scientific dictionary. 2008.

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  • Irreducible (mathematics) — In mathematics, the term irreducible is used in several ways. * In abstract algebra, irreducible can be an abbreviation for irreducible element; for example an irreducible polynomial. * In representation theory, an irreducible representation is a …   Wikipedia

  • Module (mathematics) — For other uses, see Module (disambiguation). In abstract algebra, the concept of a module over a ring is a generalization of the notion of vector space, wherein the corresponding scalars are allowed to lie in an arbitrary ring. Modules also… …   Wikipedia

  • Verma module — Verma modules, named after Daya Nand Verma, are objects in the representation theory of Lie algebras, a branch of mathematics. The definition of a Verma module looks complicated, but Verma modules are very natural objects, with useful properties …   Wikipedia

  • Semisimple module — In mathematics, especially in the area of abstract algebra known as module theory, a semisimple module or completely reducible module is a type of module that can be understood easily from its parts. A ring which is a semisimple module over… …   Wikipedia

  • Simple module — In abstract algebra, a (left or right) module S over a ring R is called simple or irreducible if it is not the zero module 0 and if its only submodules are 0 and S . Understanding the simple modules over a ring is usually helpful because these… …   Wikipedia

  • Demazure module — In mathematics, a Demazure module, introduced by Demazure (1974a, 1974b). is a submodule of a finite dimensional representation generated by an extremal weight space under the action of a Borel subalgebra. The Demazure character formula,… …   Wikipedia

  • Generalized Verma module — Generalized Verma modules are object in the representation theory of Lie algebras, a field in mathematics. They were studied originally by James Lepowsky in seventies. The motivation for their study is that their homomorphisms correspond to… …   Wikipedia

  • Core (group) — In group theory, a branch of mathematics, a core is any of certain special normal subgroups of a group. The two most common types are the normal core of a subgroup and the p core of a group. Contents 1 The normal core 1.1 Definition 1.2… …   Wikipedia

  • Schur–Weyl duality — is a mathematical theorem in representation theory that relates irreducible finite dimensional representations of the general linear and symmetric groups. It is named after two pioneers of representation theory of Lie groups, Issai Schur, who… …   Wikipedia

  • Jacobson density theorem — In mathematics, the Jacobson density theorem in ring theory is an important generalization of the Artin Wedderburn theorem. It is named for Nathan Jacobson.It states that given any irreducible module M for a ring R , R is dense in its bicommutant …   Wikipedia

  • Modular representation theory — is a branch of mathematics, and that part of representation theory that studies linear representations of finite group G over a field K of positive characteristic. As well as having applications to group theory, modular representations arise… …   Wikipedia


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