In this note we shall show that this theorem is valid for any, not necessarily semi-simple, Lie algebra. From this we see easily that the decomposition of a Lie algebra into the eigen-spaces of a maximal nilpotent subalgebra containing a regular element (Cartan decomposition) is unique up ...
A Cartan decomposition is a vector space decompositiong=t⊕p, where[i]tis a subalgebra,[ii]pis a subspace,[iii][t,p] ⊆p,[iv][p,p] ⊆ t,[v]the Killing form is negative-definite ontand[vi]Killing form ispositive-definite onp. Examples > withDifferentialGeometry&colon...
1) Cartan decomposition Cartan分解1. In this paper,we give the conceptions of real form and Cartan decomposition of affine Kac-Moody Lie algebras,discuss the real form and give all Cartan decomposition of affine Kac-Moody Lie algebras. 将实形式与Cartan分解等概念推广到仿射Kac Moody李代数,系统...
3) cartan subalgebra 嘉当子代数4) cartan decomposition 嘉当分解5) cartan formula 嘉当公式6) Cartan matrix 嘉当矩阵补充资料:嘉当 嘉当(1869～1951)Cartam,lie-Joseph 法国数学家。1869年4月9日生于伊泽尔的多洛米约,1951年5月6日卒于巴黎。1891年毕业于巴黎高等师范学校,1894年获博士学位后,先后执教...
PosRts - a list of Vectors, specifying a choice of positive roots for the root space decomposition Description Examples Description • Let g be a semi-simple, real Lie algebra. Then g is called compact if the Killing form ,of g is negative-definite, otherwise g is called non-...
on the classification of simple amenable c*-algebras with finite decomposition rank, ii, preprint. arxiv:1507.03437v3 gardella, e.: compact group actions on c*-algebras: classification, non-classifiability, and crossed products and rigidity results for \(l^p\) -operator algebras, ph.d. ...
Let L = X(m; n), X u2208 {W, S, H, K}, be a graded simple Lie algebra of Cartan type over an algebraically closed field of characteristic p > 3. Then L is ... B Shu,YF Yao - 《Journal of Algebra & Its Applications》 被引量: 1发表: 2014年 Decomposition Numbers and Cartan...
arXiv:hep-th/0212347 and arXiv:hep-th/0401033v2 can be generalized so that they permit to study the expansion of algebras of loops, both when the compact finite-dimensional algebra and the algebra of loops have a decomposition into two subspaces....
We prove that for any free ergodic nonsingular nonamenable action Γ↷(X,μ) of all Γ in a large class of groups including all hyperbolic groups, the associated group measure space von Neumann algebra L∞(X)⋊Γ has L∞(X) as its unique Cartan subalgebra, up to unitary conjugacy....
Let ℑ be a nilpotent subalgebra of a Leibniz algebra L and L = L 0 ⊕L 1 be the Fitting’s decomposition of the algebra L with respect to the nilpotent Lie algebra R(ℑ) = {R x | x ∈ ℑ} of transformations of the vector space as in theorem 2.1. The set l(ℑ) = ...