semisimple element
61Simple algebra — In mathematics, specifically in ring theory, an algebra is simple if it contains no non trivial two sided ideals and the set { ab | a , b are elements of the algebra} ne; {0}.The second condition in the definition precludes the following… …
62Approximation in algebraic groups — In mathematics, strong approximation in linear algebraic groups is an important arithmetic property of matrix groups. In rough terms, it explains to what extent there can be an extension of the Chinese remainder theorem to various kinds of… …
63Harish-Chandra homomorphism — In mathematics, the Harish Chandra homomorphismis an isomorphism of commutative rings constructed in the theory of Lie algebras. The isomorphism maps the center Z ( U ( g )) of the universal enveloping algebra U ( g ) of a semisimple Lie algebra… …
64Graded Lie algebra — In mathematics, a graded Lie algebra is a Lie algebra endowed with a gradation which is compatible with the Lie bracket. In other words, a graded Lie algebra is a Lie algebra which is also a nonassociative graded algebra under the bracket… …
65Langlands classification — In mathematics, the Langlands classification is a classification of irreducible representations of a reductive Lie group G , suggested by Robert Langlands (1973). More precisely, it classifies the irreducible admissible ( g , K ) modules,for g a… …
66Bruhat order — In mathematics, the Bruhat order (also called strong order or strong Bruhat order or Chevalley order or Bruhat–Chevalley order or Chevalley–Bruhat order) is a partial order on the elements of a Coxeter group, that corresponds to the inclusion… …
67Grand Unified Theory — For the album, see Grand Unification (album). Beyond the Standard Model …
68Ring theory — In abstract algebra, ring theory is the study of rings algebraic structures in which addition and multiplication are defined and have similar properties to those familiar from the integers. Ring theory studies the structure of rings, their… …
69Maximal torus — In the mathematical theory of compact Lie groups a special role is played by torus subgroups, in particular by the maximal torus subgroups. A torus in a Lie group G is a compact, connected, abelian Lie subgroup of G (and therefore isomorphic to… …
70Holonomy — Parallel transport on a sphere depends on the path. Transporting from A → N → B → A yields a vector different from the initial vector. This failure to return to the initial vector is measured by the holonomy of the connection. In differential… …
