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81.
We study a boundary version of the gauged WZW model with a Poisson–Lie group G as the target. The Poisson–Lie structure of G is used to define the Wess–Zumino term of the action on surfaces with boundary. We clarify the relation of the model to the topological Poisson sigma model with the dual Poisson–Lie group G
* as the target and show that the phase space of the theory on a strip is essentially the Heisenberg double of G introduced by Semenov–Tian–Shansky. 相似文献
82.
Derived Brackets 总被引:3,自引:1,他引:2
Yvette Kosmann-Schwarzbach 《Letters in Mathematical Physics》2004,69(1-3):61-87
We survey the many instances of derived bracket construction in differential geometry, Lie algebroid and Courant algebroid theories, and their properties. We recall and compare the constructions of Buttin and of Vinogradov, and we prove that the Vinogradov bracket is the skew-symmetrization of a derived bracket. Odd (resp., even) Poisson brackets on supermanifolds are derived brackets of canonical even (resp., odd) Poisson brackets on their cotangent bundle (resp., parity-reversed cotangent bundle). Lie algebras have analogous properties, and the theory of Lie algebroids unifies the results valid for manifolds on the one hand, and for Lie algebras on the other. We outline the role of derived brackets in the theory of Poisson structures with background'. 相似文献
83.
A Q-algebra can be represented as an operator algebra on an infinite dimensional Hilbert space. However we don’t know whether a finite n-dimensional Q-algebra can be represented on a Hilbert space of dimension n except n = 1, 2. It is known that a two dimensional Q-algebra is just a two dimensional commutative operator algebra on a two dimensional Hilbert space. In this paper we study a finite n-dimensional semisimple Q-algebra on a finite n-dimensional Hilbert space. In particular we describe a three dimensional Q-algebra of the disc algebra on a three dimensional Hilbert space. Our studies are related to the Pick interpolation problem for a uniform algebra. 相似文献
84.
有限维路代数的K_1群 总被引:1,自引:0,他引:1
本文通过计算有限维路代数k△的单位群和单位群的阿贝尔化,完全刻划了 任意域上有限维路代数的K1群. 相似文献
85.
Wujie Shi 《Frontiers of Mathematics in China》2007,2(1):123-125
Let G be a finite group, and let π
e
(G) be the set of all element orders of G. In this short paper we prove that π
e
(B
n
(q)) ≠ π
e
(C
n
(q)) for all odd q.
相似文献
86.
We give combinatorial proofs that certain families of differences of products of Schur functions are monomial-positive. We
show in addition that such monomial-positivity is to be expected of a large class of generating functions with combinatorial
definitions similar to Schur functions. These generating functions are defined on posets with labelled Hasse diagrams and
include for example generating functions of Stanley's (P,ω)-partitions.
T.L. was supported in part by NSF DMS-0600677. 相似文献
87.
If M is an isoparametric hypersurface in a sphere S
n
with four distinct principal curvatures, then the principal curvatures κ1, . . . , κ4 can be ordered so that their multiplicities satisfy m
1 = m
2 and m
3 = m
4, and the cross-ratio r of the principal curvatures (the Lie curvature) equals −1. In this paper, we prove that if M is an irreducible connected proper Dupin hypersurface in R
n
(or S
n
) with four distinct principal curvatures with multiplicities m
1 = m
2 ≥ 1 and m
3 = m
4 = 1, and constant Lie curvature r = −1, then M is equivalent by Lie sphere transformation to an isoparametric hypersurface in a sphere. This result remains true if the
assumption of irreducibility is replaced by compactness and r is merely assumed to be constant.
相似文献
88.
Marco Merkli 《Journal of Mathematical Analysis and Applications》2007,327(1):376-399
Level shift operators describe the second-order displacement of eigenvalues under perturbation. They play a central role in resonance theory and ergodic theory of open quantum systems at positive temperatures. We exhibit intrinsic properties of level shift operators, properties which stem from the structure of open quantum systems at positive temperatures and which are common to all such systems. They determine the geometry of resonances bifurcating from eigenvalues of positive temperature Hamiltonians and they relate the Gibbs state, the kernel of level shift operators, and zero energy resonances. We show that degeneracy of energy levels of the small part of the open quantum system causes the Fermi Golden Rule Condition to be violated and we analyze ergodic properties of such systems. 相似文献
89.
Martin I. Karakhanyan 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2007,42(3):146-150
The paper proves some general facts on commutators that refer to Fuglede-Putnam classical theorem in the spectral theory of not necessarily selfadjoint operators. 相似文献
90.
We continue to investigate strongly and weakly Lie remarkable equations, which we defined in a recent paper. We consider some
relevant algebras of vector fields on ℝk (such as the isometric, affine, projective, or conformal algebras) and characterize strongly Lie remarkable equations admitted
by the considered Lie algebras.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 151, No. 3, pp. 486–494, June, 2007. 相似文献