共查询到20条相似文献,搜索用时 15 毫秒
1.
《Communications in Nonlinear Science & Numerical Simulation》2011,16(4):1734-1741
A 3 × 3 Lie algebra H is introduced whose induced Lie algebra by decomposition and linear combinations is obtained, which may reduce to the Lie algebra given by AP Fordy and J Gibbons. By employing the induced Lie algebra and the zero curvature equation, a kind of enlarged Boussinesq soliton hierarchy is produced. Again making use of a subalgebra of the induced Lie algebra leads to the well-known KdV hierarchy whose expanding integrable system is also worked out. As an applied example of the Lie algebra H, we obtain a new integrable coupling of the well-known AKNS hierarchy. 相似文献
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Yu. A. Chapovskii 《Ukrainian Mathematical Journal》1994,46(8):1157-1171
We consider a pair of a compact quantum group and a coideal in its dual Hopf *-algebra and introduce the notions of Gelfand pair and strict Gelfand pair. For a strict Gelfand pair, we construct two hyper-complex systems dual to each other. As an example, we consider the quantum analog of the pair (U(n), SO(n)).Published in Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 8, pp. 1055–1066, August, 1994.This research was partially supported by the Foundation for Fundamental Researches of the Ukrainian State Committee on Science and Technology (Project 1/238 Operator). 相似文献
4.
Justyna Kosakowska 《数学学报(英文版)》2008,24(10):1687-1702
In the present paper we describe a specialization of prinjective Ringel-Hall algebra to 1, for prinjective modules over incidence algebras of posets of finite prinjective type, by generators and relations. This gives us a generalisation of Serre relations for semisimple Lie algebras. Connections of prinjective Ringel-Hall algebras with classical Lie algebras are also discussed. 相似文献
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We study a D-dimensional cosmological model on the manifold M=ℝ×M0×˯×Mn describing an evolution of n+1 Einstein factor spaces Mi in a theory with several dilatonic scalar fields and differential forms admitting an interpretation in terms of intersecting p-branes. The equations of motion of the model are reduced to the Euler-Lagrange equations for the so-called pseudo-Euclidean Toda-like system. Assuming that the characteristic vectors related to the configuration of p-branes and their couplings to the dilatonic scalar fields can be interpreted as the root vectors of a Lie algebra of the type Am≡sl(m+1,ℂ), we reduce the model to an open Toda chain, which is integrable by the customary methods. The resulting metric has the form of the Kasner solution. We single out the particular model describing the Friedmanlike evolution of the three-dimensional external factor space M0 (in the Einsteinian conformal gauge) and the contraction of the internal factor spaces M1,…,Mn. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 123, No. 3, pp. 374–394, June, 2000. 相似文献
7.
V. A. Zolotarev 《Journal of Mathematical Sciences》1997,85(5):2203-2207
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We show in a certain Lie*-algebra, the connections between the Lie subalgebra G
+:= G + G* + [G, G*], generated by a Lie subalgebra G, and the properties of G. This allows us to investigate some useful information about the structure of such two Lie subalgebras. Some results on the
relations between the two Lie subalgebras are obtained. As an application, we get the following conclusion: Let A ⊂ B(X) be a space of self-adjoint operators and ℒ:= A ⊕ iA the corresponding complex Lie*-algebra. G
+ = G + G* + [G, G*] and G are two LM-decomposable Lie subalgebras of ℒ with the decomposition G
+ = R(G
+) + S, G = R
G
+ S
G
, and R
G
⊆ R(G
+). Then G
+ is ideally finite iff R
G
+:= R
G
+ R*
G
* + [R
G
, R
G
*] is a quasisolvable Lie subalgebra, S
G
+:= S
G
+ S
G
* + [S
G
, S
G
*] is an ideally finite semisimple Lie subalgebra, and [R
G
, S
G
] = [R
G
*, S
G
] = {0}. 相似文献
10.
M. Beattie S. Dascalescu S. Raianu 《Proceedings of the American Mathematical Society》2000,128(11):3201-3203
If is a co-Frobenius Hopf algebra over a field, having a Galois -object which is separable over , its ring of coinvariants, then is finite dimensional.
11.
WU ZhiXiang 《中国科学 数学(英文版)》2010,(5)
Suppose that H is a Hopf algebra,and g is a generalized Kac-Moody algebra with Cartan matrix A =(aij)I×I,where I is an index set and is equal to either {1,2,...,n} or the natural number set N.Let f,g be two mappings from I to G(H),the set of group-like elements of H,such that the multiplication of elements in the set {f(i),g(i)|i ∈I} is commutative.Then we define a Hopf algebra Hgf Uq(g),where Uq(g) is the quantized enveloping algebra of g. 相似文献
12.
This paper defines a remarkable Lie algebra of infinite dimension and rank, and conjectures that it may be related to the Fischer-Griess Monster group. 相似文献
13.
余德民 《纯粹数学与应用数学》2014,30(4):341-346
构造了一类无限维李代数,它是Virasoro-like李代数的推广.研究了这类李代数的两类自同构,这两类自同构均关于映射的合成构成自同构群,一类同构于对称群S3,另一类同构于Klein交换群.得到了这类李代数一些特殊的自同态、中心.证明了这类李代数不是半单李代数. 相似文献
14.
Cycles, also known as self-avoiding polygons, elementary circuits or simple cycles, are closed walks which are not allowed to visit any vertex more than once. We present an exact formula for enumerating such cycles of any length on any directed graph involving a sum over its induced subgraphs. This result stems from a Hopf algebra, which we construct explicitly, and which provides further means of counting cycles. Finally, we obtain a more general theorem asserting that any Lie idempotent can be used to enumerate cycles. 相似文献
15.
Finite groups acting on rings by automorphisms, and group-graded rings are instances of Hopf algebras H acting on H-module algebras A. We study such actions. Let AH = {a ε A¦h · A = (h) a, all h ε H}, the ring of H-invariants, and form the smash product A # H. We study the ring extensions AH A A # H. We prove a Maschke-type theorem for A # H-modules. We form an associated Morita context [AH, A, A, A # H] and use these to get connections between the various rings. 相似文献
16.
Abstract. Each choice of a K?hler class on a compact complex manifold defines an action of the Lie algebra sl(2) on its total complex cohomology. If a nonempty set of such K?hler classes is given, then we prove that the corresponding
sl(2)-copies generate a semisimple Lie algebra. We investigate the formal properties of the resulting representation and we
work things out explicitly in the case of complex tori, hyperk?hler manifolds and flag varieties. We pay special attention
to the cases where this leads to a Jordan algebra structure or a graded Frobenius algebra.
Oblatum 21-V-1996 & 15-X-1996 相似文献
17.
Shundong Zhu Shoufeng Shen Yongyang Jin Chunxia Li Wen‐Xiu Ma 《Mathematical Methods in the Applied Sciences》2017,40(3):680-698
We present some new matrix spectral problems, based on the real special orthogonal Lie algebra , and construct corresponding soliton hierarchies by means of zero curvature equations associated with these spectral problems. With the aid of symbolic computation by Maple, new soliton hierarchies of Kaup–Newell type, Ablowitz–Kaup–Newell–Segur type and Wadati–Konno–Ichikawa type are obtained to illustrate the use of . Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
18.
Yongchang Zhu 《Proceedings of the American Mathematical Society》1997,125(10):2847-2851
We prove that if is a semisimple Hopf algebra, then the action of the Drinfeld double on and the action of the character algebra on form a commuting pair. This result and a result of G. I. Kats imply that the dimension of every simple -submodule of is a divisor of .
19.
To a semisimple and cosemisimple Hopf algebra over an algebraically closed field, we associate a planar algebra defined by
generators and relations and show that it is a connected, irreducible, spherical, non-degenerate planar algebra with non-zero
modulus and of depth two. This association is shown to yield a bijection between (the isomorphism classes, on both sides,
of) such objects. 相似文献