noncommutative group

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• Noncommutative algebraic geometry — is a branch of mathematics, and more specifically a direction in noncommutative geometry that studies the geometric properties of formal duals of non commutative algebraic objects such as rings as well as geometric objects derived from them (e.g …   Wikipedia

• Noncommutative ring — In mathematics, more specifically modern algebra and ring theory, a noncommutative ring is a ring whose multiplication is not commutative; that is, if R is a noncommutative ring, there exists a and b in R with a·b ≠ b·a, and conversely.… …   Wikipedia

• Noncommutative geometry — Not to be confused with Anabelian geometry. Noncommutative geometry (NCG) is a branch of mathematics concerned with geometric approach to noncommutative algebras, and with construction of spaces which are locally presented by noncommutative… …   Wikipedia

• Noncommutative standard model — In theoretical particle physics, the non commutative Standard Model, mainly due to the French mathematician Alain Connes, uses his noncommutative geometry to devise an extension of the Standard Model to include a modified form of general… …   Wikipedia

• Noncommutative harmonic analysis — In mathematics, noncommutative harmonic analysis is the field in which results from Fourier analysis are extended to topological groups which are not commutative. Since for locally compact abelian groups have a well understood theory, Pontryagin… …   Wikipedia

• Group Hopf algebra — In mathematics, the group Hopf algebra of a given group is a certain construct related to the symmetries of group actions. Deformations of group Hopf algebras are foundational in the theory of quantum groups. DefinitionLet G be an arbitrary group …   Wikipedia

• Quantum group — In mathematics and theoretical physics, quantum groups are certain noncommutative algebras that first appeared in the theory of quantum integrable systems, and which were then formalized by Vladimir Drinfel d and Michio Jimbo. There is no single …   Wikipedia

• Butcher group — In mathematics, the Butcher group, named after the New Zealand mathematician John C. Butcher by Hairer Wanner (1974), is an infinite dimensional group first introduced in numerical analysis to study solutions of non linear ordinary differential… …   Wikipedia

• Depth of noncommutative subrings — In ring theory and Frobenius algebra extensions, fields of mathematics, there is a notion of depth two subring or depth of a Frobenius extension. The notion of depth two is important in a certain noncommutative Galois theory, which generates Hopf …   Wikipedia

• Free group — In mathematics, a group G is called free if there is a subset S of G such that any element of G can be written in one and only one way as a product of finitely many elements of S and their inverses (disregarding trivial variations such as st 1 =… …   Wikipedia

• Elementary group theory — In mathematics, a group is defined as a set G and a binary operation on G , called product and denoted by infix * . Product obeys the following rules (also called axioms). Let a , b , and c be arbitrary elements of G . Then: *A1, Closure. a * b… …   Wikipedia