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51.
《Indagationes Mathematicae》2022,33(3):598-624
We construct left invariant special Kähler structures on the cotangent bundle of a flat pseudo-Riemannian Lie group. We introduce the twisted cartesian product of two special Kähler Lie algebras according to two linear representations by infinitesimal Kähler transformations. We also exhibit a double extension process of a special Kähler Lie algebra which allows us to get all simply connected special Kähler Lie groups with bi-invariant symplectic connections. All Lie groups constructed by performing this double extension process can be identified with a subgroup of symplectic (or Kähler) affine transformations of its Lie algebra containing a nontrivial 1-parameter subgroup formed by central translations. We show a characterization of left invariant flat special Kähler structures using étale Kähler affine representations, exhibit some immediate consequences of the constructions mentioned above, and give several non-trivial examples. 相似文献
52.
53.
Mark Curtis Wilson 《Proceedings of the American Mathematical Society》1996,124(2):383-387
We show that a primeness criterion for enveloping algebras of Lie superalgebras discovered by Bell is applicable to the Cartan type Lie superalgebras , even. Other algebras are considered but there are no definitive answers in these cases.
54.
One-parameter semigroups occurring in operator-limit distributions are investigated. The topological-algebraic background of the relevant monoids is discussed and Lie semigroup theory is applied to the Urbanik Decomposability Semigroup. 相似文献
55.
C.K. Fan 《Journal of Algebraic Combinatorics》1996,5(3):175-189
Let (W, S) be a Coxeter group associated to a Coxeter graph which has no multiple bonds. Let H be the corresponding Hecke Algebra. We define a certain quotient \-H of H and show that it has a basis parametrized by a certain subset W
cof the Coxeter group W. Specifically, W
cconsists of those elements of W all of whose reduced expressions avoid substrings of the form sts where s and t are noncommuting generators in S. We determine which Coxeter groups have finite W
cand compute the cardinality of W
cwhen W is a Weyl group. Finally, we give a combinatorial application (which is related to the number of reduced expressions for w W
cof an exponential formula of Lusztig which utilizes a specialization of a subalgebra of \-H. 相似文献
56.
Janusz Grabowski 《Annals of Global Analysis and Geometry》1993,11(3):213-220
It is proved that for infinite dimensional Lie groups in the sense of the differential calculus of Frölicher and Kriegl the derivative of the exponential mappings is given by the formula d(exp)(X)Y=dexp(X)(e)
0
1
Adexp(–tX)
Y dt, where stands for the left translation ande is the neutral element.This work was supported by the Alexander von Humboldt-Stiftung. 相似文献
57.
58.
59.
提出了一种动力学李代数方法来研究取代苯体系的非线性光学性质. 对于给定的PPP模型(Pariser-Parr-Pople)哈密顿量, 生成了一个动力学李代数. 依据这些代数元构造出演化算子作为群参数的函数, 通过求解一组非线性微分方程能够得到这些群参数. 再按照统计力学中的密度算子公式给出取代苯分子体系偶极矩的统计平均值. 于是导出二阶极化率的表达式. 与其他量子力学计算结果比较, 表明这种动力学李代数方法在预言有机共轭分子的非线性光学性质上同样有用. 相似文献
60.
Xian Zhao Daren Guan Xizhang Yi Guibao Xu Minhua Jiang 《International journal of quantum chemistry》2003,93(5):335-343
A dynamic Lie algebraic (DLA) formulation is applied to the study of nonlinear optical properties of the substituted benzenes. We have described the generation of the dynamic Lie algebra for the model Hamiltonian used in the present study. In terms of these elements of the dynamic algebra we express the evolution operator as a function of the group parameters, which can be determined by means of solving a system of coupled nonlinear differential equations. Thus, in terms of the density matrix operator formalism in statistical mechanics we obtain the statistical averages of the electric polarization and then derive readily an expression for the hyperpolarizability of the paradisubstituted benzenes. Comparisons with experimental observations and other quantum calculations of the hyperpolarizabilities for the paradisubstituted benzenes are made qualitatively and quantitatively. These results imply that the DLA method appears useful in describing the nonlinear optical phenomena in the substituted benzene molecules. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 93: 335–343, 2003 相似文献