- finite-dimensional Lie algebra
- конечномерная алгебра Ли
English-russian dictionary of physics. 2013.
finite-dimensional Lie algebra
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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
Compact Lie algebra — Lie groups … Wikipedia
Lie algebra representation — Lie groups … Wikipedia
Semisimple Lie algebra — In mathematics, a Lie algebra is semisimple if it is a direct sum of simple Lie algebras, i.e., non abelian Lie algebras mathfrak g whose only ideals are {0} and mathfrak g itself. It is called reductive if it is the sum of a semisimple and an… … 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
Nilpotent Lie algebra — In mathematics, a Lie algebra is nilpotent if the lower central series becomes zero eventually. Equivalently, is nilpotent if … Wikipedia
Nilradical of a Lie algebra — In algebra, the nilradical of a Lie algebra is a nilpotent ideal, which is as large as possible. The nilradical of a finite dimensional Lie algebra is its maximal nilpotent ideal, which exists because the sum of any two nilpotent ideals is… … Wikipedia
Lie group — Lie groups … Wikipedia
Affine Lie algebra — In mathematics, an affine Lie algebra is an infinite dimensional Lie algebra that is constructed in a canonical fashion out of a finite dimensional simple Lie algebra. It is a Kac–Moody algebra whose generalized Cartan matrix is positive semi… … Wikipedia
En (Lie algebra) — In mathematics, especially in Lie theory, E n is the Kac–Moody algebra whose Dynkin diagram is a line of n 1 points with an extra point attached to the third point from the end. Finite dimensional Lie algebras*E3 is another name for the Lie… … Wikipedia
Lie group decomposition — In mathematics, Lie group decompositions are used to analyse the structure of Lie groups and associated objects, by showing how they are built up out of subgroups. They are essential technical tools in the representation theory of Lie groups and… … Wikipedia
