solvable radical
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Radical of a Lie algebra — The radical of a Lie algebra mathfrak{g} is a particular ideal of mathfrak{g}. Definition Let mathfrak{g} be a Lie algebra. The radical of mathfrak{g} is defined as the largest solvable ideal of mathfrak{g}.Such an ideal exists for the following… … Wikipedia
Solvable Lie algebra — In mathematics, a Lie algebra g is solvable if its derived series terminates in the zero subalgebra. That is, writing for the derived Lie algebra of g, generated by the set of values [x,y] for x and y in g, the derived series … 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
Bring radical — In algebra, a Bring radical or ultraradical is a root of the polynomial :x^5+x+a, ,where a is a complex number. (The root is chosen so the radical of a real is real, and the radical is a differentiable function of a in the complex plane, with a… … Wikipedia
Lie algebra — In mathematics, a Lie algebra is an algebraic structure whose main use is in studying geometric objects such as Lie groups and differentiable manifolds. Lie algebras were introduced to study the concept of infinitesimal transformations. The term… … 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
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
Quintic equation — In mathematics, a quintic equation is a polynomial equation of degree five. It is of the form::ax^5+bx^4+cx^3+dx^2+ex+f=0, where a e 0.(if a = 0, then the equation becomes a quartic equation). (if a and b = 0, then the equation becomes a cubic… … Wikipedia
mathematics — /math euh mat iks/, n. 1. (used with a sing. v.) the systematic treatment of magnitude, relationships between figures and forms, and relations between quantities expressed symbolically. 2. (used with a sing. or pl. v.) mathematical procedures,… … Universalium
algebra — /al jeuh breuh/, n. 1. the branch of mathematics that deals with general statements of relations, utilizing letters and other symbols to represent specific sets of numbers, values, vectors, etc., in the description of such relations. 2. any of… … Universalium
Levi decomposition — In Lie theory and representation theory, the Levi decomposition, discovered by Eugenio Elia Levi (1906), states that any finite dimensional real Lie algebra g is (as a vector space) the direct sum of two significant structural parts; namely,… … Wikipedia
