共查询到20条相似文献,搜索用时 62 毫秒
1.
Wolfgang Bock Vyacheslav Futorny Mikhail Neklyudov 《Journal of Pure and Applied Algebra》2021,225(3):106535
A realization by linear vector fields is constructed for any Lie algebra which admits a biorthogonal system and for its any suitable representation. The embedding into Lie algebras of linear vector fields is in analogue to the classical Jordan—Schwinger map. A number of examples of such Lie algebras of linear vector fields is computed. In particular, we obtain examples of the twisted Heisenberg-Virasoro Lie algebra and the Schrödinger-Virasoro Lie algebras among others. More generally, we construct an embedding of an arbitrary locally convex topological algebra into the Cuntz algebra. 相似文献
2.
In this paper, we use the general quantization method by Drinfel’d twists to quantize the Schrödinger-Virasoro Lie algebra whose Lie bialgebra structures were recently discovered by Han-Li-Su. We give two different kinds of Drinfel’d twists, which are then used to construct the corresponding Hopf algebraic structures. Our results extend the class of examples of noncommutative and noncocommutative Hopf algebras. 相似文献
3.
In this paper, we investigate Lie bialgebra structures on a twisted Schr?dinger-Virasoro type algebra L . All Lie bialgebra structures on L are triangular coboundary, which is different from the relative result on the original Schr?dinger-Virasoro type Lie algebra. In particular, we find for this Lie algebra that there are more hidden inner derivations from itself to L ? L and we develop one method to search them. 相似文献
4.
董泉发 《数学年刊A辑(中文版)》2015,36(3):325-334
构造了Cartan型李代数W(n;m)的一类Borel子代数φ(n;m),其中n是一个正整数,且m=(m_1,…,m_n)是一个n-元正整数数组.确定了φ(n;m)的导子代数.特别地,φ(n;1)是一个Cartan型完备阶化李代数,它不同于任何典型完备李代数. 相似文献
5.
WU MING-ZHONG 《东北数学》2009,25(1)
In this paper, we study the Lie algebras in which every subspace is its subalgebra (denoted by HB Lie algebras). We get that a nonabelian Lie algebra is an HB Lie algebra if and only if it is isomorphic to g+Cidg, where g is an abelian Lie algebra. Moreover we show that the derivation algebra and the holomorph of a nonabelian HB Lie algebra are complete. 相似文献
6.
It is shown that the support of an irreducible weight module over the SchrSdinger-Virasoro Lie algebra with an infinite-dimensional weight space coincides with the weight lattice, and all nontrivial weight spaces of such a module are infinite-dimensional. As a by-product, it is obtained that every simple weight module over Lie algebra of this type with a nontrivial finite-dimensional weight space is a Harish-Chandra module. 相似文献
7.
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
8.
Mingzhong Wu 《数学研究通讯:英文版》2009,25(1):1-8
In this paper, we study the Lie algebras in which every subspace is its
subalgebra (denoted by HB Lie algebras). We get that a nonabelian Lie algebra is
an HB Lie algebra if and only if it is isomorphic to $g\dot{+}\mathbb{C}id_g$, where $g$ is an abelian
Lie algebra. Moreover we show that the derivation algebra and the holomorph of a
nonabelian HB Lie algebra are complete. 相似文献
9.
10.
11.
求出了(n-3)-filiform李代数的极大环面,并证明了(n-3)-filiform李代数是可完备化的. 相似文献
12.
In this article,we compute cohomology groups of the semisimple Lie conformal algebra S =Vir × Cur g with coefficients in its irreducible modules for a finite-dimensional simple Lie algebra g. 相似文献
13.
无限维Heisenberg代数的导子代数和全形 总被引:2,自引:0,他引:2
给出了无维Heisrberg代数的全形和全形的导子代数Der(s)证明(s)不是一个完备李代数,但Der(s)是一个完备李代数。 相似文献
14.
Poisson代数是指同时具有代数结构和李代数结构的一类代数,其乘法与李代数乘法满足Leibniz法则.扭Heisenberg-Virasoro代数是一类重要的无限维李代数,是次数不超过1的微分算子李代数W(0)的普遍中心扩张,与曲线的模空间有密切联系.本文主要研究扭Heisenberg-Virasoro代数上的Poisson结构,首先确定了李代数W(0)上的Poisson结构,进而给出了扭Heisenberg-Virasoro代数上的Poisson结构. 相似文献
15.
In this paper, by using Gröbner–Shirshov bases theories, we prove that each countably generated associative algebra (Lie algebra) can be embedded into a simple two-generated associative algebra (Lie algebra). 相似文献
16.
We investigate the nilpotence of a Malcev algebra M and of its standard enveloping Lie algebra L(M)=M D(M, M). The main result shows that an ideal A of M is nilpotent in M if and only if the corresponding ideal Ⅰ(A) = A D(A, M)is nilpotent in L(M). 相似文献
17.
Mingzhong Wu 《数学研究通讯:英文版》2012,28(3):218-224
In this paper we explicitly determine the derivation algebra of a quasi $R_n$-filiform Lie algebra and prove that a quasi $R_n$-filiform Lie algebra is a completable
nilpotent Lie algebra. 相似文献
18.
S. T. Sadetov 《Functional Analysis and Its Applications》2007,41(1):42-53
Let \(\mathfrak{n}\) be a finite-dimensional noncommutative nilpotent Lie algebra for which the ring of polynomial invariants of the coadjoint representation is generated by linear functions. Let \(\mathfrak{g}\) be an arbitrary Lie algebra. We consider semidirect sums \(\mathfrak{n} \dashv _\rho \mathfrak{g}\) with respect to an arbitrary representation ρ: \(\mathfrak{g}\) → der \(\mathfrak{n}\) such that the center z \(\mathfrak{n}\) of \(\mathfrak{n}\) has a ρ-invariant complement.We establish that some localization \(\tilde P(\mathfrak{n} \dashv _\rho \mathfrak{g})\) of the Poisson algebra of polynomials in elements of the Lie algebra \(\mathfrak{n} \dashv _\rho \mathfrak{g}\) is isomorphic to the tensor product of the standard Poisson algebra of a nonzero symplectic space by a localization of the Poisson algebra of the Lie subalgebra \((z\mathfrak{n}) \dashv \mathfrak{g}\). If \([\mathfrak{n},\mathfrak{n}] \subseteq z\mathfrak{n}\), then a similar tensor product decomposition is established for the localized universal enveloping algebra of the Lie algebra \(\mathfrak{n} \dashv _\rho \mathfrak{g}\). For the case in which \(\mathfrak{n}\) is a Heisenberg algebra, we obtain explicit formulas for the embeddings of \(\mathfrak{g}_P \) in \(\tilde P(\mathfrak{n} \dashv _\rho \mathfrak{g})\). These formulas have applications, some related to integrability in mechanics and others to the Gelfand-Kirillov conjecture. 相似文献
19.
U(g_((+)))的极小生成元和生成关系 总被引:1,自引:1,他引:0
刘雪梅 《数学的实践与认识》2012,42(9):203-206
设g是有限维单李代数,g是相应于g的无扭仿型Kac-Moody代数的导代数.讨论了g的子代数g(+)的普遍包络代数U(g(+))的极小生成元和生成关系问题,证明了U(g(+))由a t~m,h t~n及1生成,其中m,n∈Z-∪{0}. 相似文献
20.
A. V. Gavriliov 《Algebra and Logic》2008,47(5):321-329
A framed Lie algebra is an algebra with two operations which is a Lie algebra with respect to one of these operations. A basic
example is a Lie algebra of vector fields on a manifold with connection where the covariant derivative serves as an additional
operation. In a free framed Lie algebra, we distinguish a set of special polynomials that geometrically correspond to invariantly
defined tensors. A necessary condition of being special is derived, and we presume that this condition is also sufficient.
Translated from Algebra i Logika, Vol. 47, No. 5, pp. 571–583, September–October, 2008. 相似文献