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In mathematics, a toral subalgebra is a Lie subalgebra of a general linear Lie algebra all of whose elements are semisimple (or diagonalizable over an...

Cartan subalgebra.pg 231 In general, a subalgebra is called toral if it consists of semisimple elements. Over an algebraically closed field, a toral subalgebra...

certain distinguished subalgebra on it, a Cartan subalgebra. By definition, a Cartan subalgebra (also called a maximal toral subalgebra) h {\displaystyle...

{g'}}]\subseteq {\mathfrak {g'}}.} Tits Tits cone. toral 1.  toral Lie algebra 2.  maximal toral subalgebra Unitarian trick Verma module Weyl 1.  Hermann Weyl...

{\displaystyle e^{-i\theta }} . Compact group Cartan subgroup Cartan subalgebra Toral Lie algebra Bruhat decomposition Weyl character formula Representation...

given a maximal Abelian subalgebra a {\displaystyle {\mathfrak {a}}} in t, A = exp a {\displaystyle {\mathfrak {a}}} is a toral subgroup such that σ(a)...

Abelian subalgebra a {\displaystyle {\mathfrak {a}}} in p {\displaystyle {\mathfrak {p}}} , A = exp a {\displaystyle {\mathfrak {a}}} is a toral subgroup...

decomposition of an algebra is a way of writing in it in terms of polynomial subalgebras. reflexive A module M is reflexive if the canonical map M → M ∗ ∗ , m...