irreducible mapping
41Group action — This article is about the mathematical concept. For the sociology term, see group action (sociology). Given an equilateral triangle, the counterclockwise rotation by 120° around the center of the triangle acts on the set of vertices of the… …
42Group ring — This page discusses the algebraic group ring of a discrete group; for the case of a topological group see group algebra, and for a general group see Group Hopf algebra. In algebra, a group ring is a free module and at the same time a ring,… …
43Stone duality — In mathematics, there is an ample supply of categorical dualities between certain categories of topological spaces and categories of partially ordered sets. Today, these dualities are usually collected under the label Stone duality, since they… …
44Creative industries — The creative industries refers to a range of economic activities which are concerned with the generation or exploitation of knowledge and information. They may variously also be referred to as the cultural industries (especially in Europe… …
45SL2(R) — In mathematics, the special linear group SL2(R) is the group of all real 2 times; 2 matrices with determinant one:: mbox{SL} 2(mathbb{R}) = left{ egin{bmatrix}a b c dend{bmatrix} : a,b,c,dinmathbb{R}mbox{ and }ad bc=1 ight}.It is a real Lie… …
46Ping-pong lemma — In mathematics, the ping pong lemma, or table tennis lemma, is any of several mathematical statements which ensure that several elements in a group acting on a set freely generate a free subgroup of that group.HistoryThe ping pong argument goes… …
47Field (mathematics) — This article is about fields in algebra. For fields in geometry, see Vector field. For other uses, see Field (disambiguation). In abstract algebra, a field is a commutative ring whose nonzero elements form a group under multiplication. As such it …
48Quasigroup — In mathematics, especially in abstract algebra, a quasigroup is an algebraic structure resembling a group in the sense that division is always possible. Quasigroups differ from groups mainly in that they need not be associative. A quasigroup with …
49Module (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… …
50Representation theory of diffeomorphism groups — In mathematics, a source for the representation theory of the group of diffeomorphisms of a smooth manifold M is the initial observation that (for M connected) that group acts transitively on M .HistoryA survey paper from 1975 of the subject by… …
