In this paper, we study Leibniz algebras $\\mathfrak{g}$ with a non-degenerate Leibniz-symmetric $\\mathfrak{g}$-invariant bilinear form B, such a pair $(\\mathfrak{g},B)$ is called a quadratic Leibniz algebra. Our first result generalizes the notion of double extensions to quadratic...
We call bilinear form over E any map b : E × E ↦ ℝ that is bilinear, i.e. linear with respect to each of its arguments. A bilinear form is called: 1) symmetric when ∀x, y∈ E, b(x, y) = b(y, x); 2) nondegenerate when ∀x∈ E, [∀y∈ E, b(x, y) ...
1.non-degenerate symmetric bilinear form非退化对称双线性型 2.On Nondegenerate Representation of Some Hilbert C~*-Module;Hilbert C~*-模上的非退化表示 3.The adjoint representations of Hopf algebras with non-degenerate Killing formKilling根非退化下Hopf代数的伴随表示 4.Co-split Lie super algebra with...
into a sum of a symmetric bilinear form g f v : V ∗ ×V ∗ →F and a skewsymmetric bilinear formh f v : V ∗ ×V ∗ →F. The bilinear alternating map f : V ×V →V is said to be non-degenerate if its symmetric part ...
美[nɒndɪdʒənə'reɪt] 英[nɒndɪdʒənə'reɪt] n.非退化;非简并 adj.〔数〕非退化的 网络简并性的 英汉 网络释义 adj. 1. 〔数〕非退化的 n. 1. 非简并 2. 非退化 释义: 全部,非退化,非简并,〔数〕非退化的,简并性的...
网络非退化二次形式;非退化二次型 网络释义
A Lie (super)algebra with a non-degenerate invariant symmetric bilinear form $B$ is called a nis-(super)algebra. The double extension $\\\mathfrak{g}$ of a nis-(super)algebra $\\\mathfrak{a}$ is the result of simultaneous adding to $\\\mathfrak{a}$ a central element and a deriv...
By definition [20, 22, 26], the rank two complex free Lie algebra is the smallest non-commutative and non-associative -algebra having and as its elements, with bilinear multiplication satisfying the skew-symmetry and Jacobi-like identity: for arbitrary elements . Such an algebra is unique up ...
1) non-degenerate bilinear form 非退化双线性型2) nonlinear degenerate hyperbolic equations 非线性退化双曲型方程3) nondegenerate sesquilinear form 非退化半双线性型;非退化半双线性形式4) non-linear regression model 非线性退化模型 1. New compound classification method for remote sensing image ...
J. Santharoubane, Symmetric, invariant, non-degenerate bilinear form on a Lie algebra, J. Algebra 105 (1987), 451-464. MR0873679Favre, G. and Santharoubane, L., Symmetric, invariant, non-degenerate bilinear form on a Lie algebra, J. Algebra, 105, 451-464 (1987)....