共查询到20条相似文献,搜索用时 31 毫秒
1.
Jin Quanqin 《代数通讯》2013,41(9):4131-4135
In this note, we give a necessary and sufficient condition for a real irreducible representation of a real simple Lie algebra to admit an invariant bilinear form. We also determine when the invariant bilinear form is symmetric or skew-symmetric. 相似文献
2.
《Journal of Pure and Applied Algebra》1994,96(3):279-297
We give a criterion for determining the existence of nonzero symmetric invariant bilinear forms on vertex operator algebras and we establish an analogue of the Cartan criterion for semi-simplicity. 相似文献
3.
In this article we study the structure of highest weight modules for quantum groups defined over a commutative ring with particular emphasis on the structure theory for invariant bilinear forms on these modules. The notion of an induced invariant form is introduced and a setting in described where all invariant forms are induced 相似文献
4.
We review the list of non-degenerate invariant (super)symmetric bilinear forms (briefly: NIS) on the following simple (relatives of) Lie (super)algebras: (a) with symmetrizable Cartan matrix of any growth, (b) with non-symmetrizable Cartan matrix of polynomial growth, (c) Lie (super)algebras of vector fields with polynomial coefficients, (d) stringy a.k.a. superconformal superalgebras, (e) queerifications of simple restricted Lie algebras. Over algebraically closed fields of positive characteristic, we establish when the deform (i.e., the result of deformation) of the known finite-dimensional simple Lie (super)algebra has a NIS. Amazingly, in most of the cases considered, if the Lie (super)algebra has a NIS, its deform has a NIS with the same Gram matrix after an identification of bases of the initial and deformed algebras. We do not consider odd parameters of deformations. Closely related with simple Lie (super)algebras with NIS is the notion of doubly extended Lie (super)algebras of which affine Kac–Moody (super)algebras are the most known examples. 相似文献
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§1. IntroductionLie algebras admitting non-degenerate and invariant bilinear forms (i.e. self-dual Liealgebras or pseudo-metric Lie algebras) has been a hot topic in the study of Lie theory. Themotivation for studying these algebras comes from the fact t… 相似文献
7.
Let \({\mathbb {F}}\) be a field, V a vector space of dimension n over \({\mathbb {F}}\). Then the set of bilinear forms on V forms a vector space of dimension \(n^2\) over \({\mathbb {F}}\). For char \({\mathbb {F}}\ne 2\), if T is an invertible linear map from V onto V then the set of T-invariant bilinear forms, forms a subspace of this space of forms. In this paper, we compute the dimension of T-invariant bilinear forms over \({\mathbb {F}}\). Also we investigate similar type of questions for the infinitesimally T-invariant bilinear forms (T-skew symmetric forms). Moreover, we discuss the existence of nondegenerate invariant (resp. infinitesimally invariant) bilinear forms. 相似文献
8.
In this paper we study the computation of symmetric systems of bilinear forms over finite fields via symmetric bilinear algorithms. We show that, in general, the symmetric complexity of a system is upper bounded by a constant multiple of the bilinear complexity; we characterize symmetric algorithms in terms of the cosets of a specific cyclic code, and we show that the problem of finding an optimal symmetric algorithm is equivalent to the maximum-likelihood decoding problem for this code. 相似文献
9.
有限维非退化可解李代数的顶点算子代数 总被引:4,自引:0,他引:4
构造相应于非退化可解李代数g的顶点算子代数分两步进行,首先构造顶点代数.本文是在已经得到的相应于非退化可解李代数g的顶点代数(Vg(l,0),Y(V,1)上构造顶点算子代数.定义了非退化可解李代数g的Casimir算子Ω,给出了在伴随表示下Ω作用在g上是0及相关性质,并应用Ω定义出Vg(l,0)中元素ω,证明了Vg(l,0)关于ω的顶点算子YV(ω,x)的系数构成一个Virasoro代数-模,还证明了ω满足顶点算子代数定义中Virasoro-向量的所有公理.从而证得(Vg(l,0),Yv,1,ω)是一个顶点算子代数. 相似文献
10.
We examine potential extensions of the Stiefel–Whitney invariants from quadratic forms to bilinear forms which are not necessarily symmetric. We show that as long as the symbolic nature of the invariants is maintained, some natural extensions carry only low dimensional information. In particular, the generic invariant on upper triangular matrices is equivalent to the dimension and determinant. Along the process, we show that every non-alternating matrix is congruent to an upper triangular matrix, and prove a version of Witt?s Chain Lemma for upper-triangular bases. (The classical lemma holds for orthogonal bases.) 相似文献
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Michael Roitman 《Journal of Pure and Applied Algebra》2004,194(3):329-345
In this paper we construct a linear space that parameterizes all invariant bilinear forms on a given vertex algebra with values in a arbitrary vector space. Also we prove that every invariant bilinear form on a vertex algebra is symmetric. This is a generalization of the result of Li (J. Pure Appl. Algebra 96(3) (1994) 279), who proved this for the case when the vertex algebra is non-negatively graded and has finite dimensional homogeneous components.As an application, we introduce a notion of a radical of a vertex algebra. We prove that a radical-free vertex algebra A is non-negatively graded, and its component A0 of degree 0 is a commutative associative algebra, so that all structural maps and operations on A are A0-linear. We also show that in this case A is simple if and only if A0 is a field. 相似文献
13.
The present paper concentrates on the analogues of Rosenthal's inequalities for ordinary and decoupled bilinear forms in symmetric random variables. More specifically, we prove the exact moment inequalities for these objects in terms of moments of their individual components. As a corollary of these results we obtain the explicit expressions for the best constant in the analogues of Rosenthal's inequality for ordinary and decoupled bilinear forms in identically distributed symmetric random variables in the case of the fixed number of random variables. 相似文献
14.
Algebras and Representation Theory - In this work we consider the moduli space of all noncommutative metric Lie algebras, having a nondegenerate symmetric invariant bilinear form, over $\mathbb C$... 相似文献
15.
本文讨论赋值环上的对称线性型、二次型和对称矩阵的合同标准形。 相似文献
16.
O. A. Ivanov 《Journal of Mathematical Sciences》1982,19(3):1250-1253
In this paper we describe a construction, associating with a pair of integral symmetric bilinear forms with identical discriminant forms, an integral symmetric unimodular bilinear form.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 83, pp. 63–66, 1979. 相似文献
17.
Andrzej Sładek 《Mathematica Slovaca》2009,59(3):291-298
In [EGAWA, Y.—SUZUKI, H.: Automorphism groups of Σ
n+1-invariant trilinear forms, Hokkaido Math. J. 11, (1985), 39–47] are explored Σ
n+1-invariant symmetric trilinear forms and their automorphisms. In the paper we generalize their results to d-linear symmetric forms for any d ≥ 3.
相似文献
18.
M. Bordemann has studied non-associative algebras with nondegenerate associative bilinear forms. In this paper, we focus on
pseudo-Riemannian bilinear forms and study pseudo-Riemannian Leibniz algebras, i.e., Leibniz algebras with pseudo-Riemannian
non-degenerate symmetric bilinear forms. We give the notion and some properties of T*-extensions of Leibniz algebras. In addition, we introduce the definition of equivalence and isometrical equivalence for
two T*-extensions of a Leibniz algebra, and give a sufficient and necessary condition for the equivalence and isometrical equivalence. 相似文献
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A module of a finite group over a finite field with a symmetric non-degenerate bilinear form which is invariant by the group action is called a symmetric module. In this paper, a characterization of indecomposable orthogonal decompositions of symmetric semisimple modules and a criterion for the hyperbolic symmetric modules are obtained, and some applications to the self-dual permutation codes are shown. 相似文献