Hecke Algebras of Group Extensions

Abstract

We describe the Hecke algebra ?(Γ,Γ₀) of a Hecke pair (Γ,Γ₀) in terms of the Hecke pair (N,Γ₀) where N is a normal subgroup of Γ containing Γ₀. To do this, we introduce twisted crossed products of unital *-algebras by semigroups. Then, provided a certain semigroup S ? Γ/N satisfies S ^?1 S = Γ/N, we show that ? (Γ,Γ₀) is the twisted crossed product of ? (N,Γ₀) by S. This generalizes a recent theorem of Laca and Larsen about Hecke algebras of semidirect products.     

(ω,σ)-Smash积积和和(ν,α)-Smash余余积积

设B,H是两个Hopf代数,构造了(ω,σ)-Smash积Bω#σH和(ν,α)-Smash余积Bν■αH,并给出了Bω#σH是Hopf代数和Bν■αH是双代数的充要条件,证明了许多已知的积和余积是它们的特殊情况.     

Geometric measure of quantum discord over two-sided projective measurements

The original definition of quantum discord of bipartite states was defined over one-sided projective measurements, it describes quantum correlations more extensively than entanglement. Dakic, Vedral, and Brukner [Phys. Rev. Lett. 105 (2010) 190502] introduced a geometric measure of quantum discord, Luo and Fu [Phys. Rev. A 82 (2010) 034302] simplified the variation expression of this geometric measure. In this Letter we introduce a geometric measure of quantum discord over two-sided projective measurements. A simplified expression and a lower bound of this two-sided geometric measure are derived and explicit expressions are obtained for some special cases.     

A note on maximality of analytic crossed products

Let G be a compact abelian group with the totally ordered dual group which admits the positive semigroup . Let N be a von Neumann algebra and be an automorphism group of on N. We denote to the analytic crossed product determined by N and α. We show that if is a maximal σ-weakly closed subalgebra of , then induces an archimedean order in .     

Eigenvectors of interval matrices over max–plus algebra

The behaviour of a discrete-event dynamic system is often conveniently described using a matrix algebra with operations max and plus. Such a system moves forward in regular steps of length equal to the eigenvalue of the system matrix, if it is set to operate at time instants corresponding to one of its eigenvectors. However, due to imprecise measurements, it is often unappropriate to use exact matrices. One possibility to model imprecision is to use interval matrices. We show that the problem to decide whether a given vector is an eigenvector of one of the matrices in the given matrix interval is polynomial, while the complexity of the existence problem of a universal eigenvector remains open. As an aside, we propose a combinatorial method for solving two-sided systems of linear equations over the max–plus algebra.     

Characterizations of the optimal stable allocation mechanism

The stable allocation problem is the generalization of (0,1)-matching problems to the allocation of real numbers (hours or quantities) between two separate sets of agents. The same unique-optimal matching (for one set of agents) is characterized by each of three properties: “efficiency”, “monotonicity”, and “strategy-proofness”.     

Multilayer mirror systems to form hard X-ray beams

This paper is an overview of the research activities carried out in the past five years at the Institute for Physics of Microstructures RAS and “X-ray” Company towards the manufacture of multilayer mirror systems capable of forming X-ray beams in the subnanometer range of wavelengths. The systems fabrication technology is presented, including techniques for producing supersmooth surfaces of specified shape, methods of graded multilayer structure deposition on such surfaces, and the principles of designing optimal mirror parameters. The characteristics of a quadrelliptical reflector—a novel high light-gathering power four-corner focusing system—are reported.     

A strongly polynomial algorithm for solving two-sided linear systems in max-algebra

An algorithm for solving m×n systems of (max,+)-linear equations is presented. The systems have variables on both sides of the equations. After O(m⁴n⁴) iterations the algorithm either finds a solution of the system or finds out that no solution exists. Each iteration needs O(mn) operations so that the complexity of the presented algorithm is O(m⁵n⁵).     

Hopf代数交叉积的同调维数

Let H be a finite dimensional cocommutative Hopf algebra and A an H-module algebra, ln this paper, we characterize the projectivity (injectivity) of M as a left A#σ H-module when it is projective (injective) as a left A-module. The sufficient and necessary condition for A#σ H, the crossed product, to have finite global homological dimension is given, in terms of the global homological dimension of A and the surjectivity of trace maps, provided that H is cocommutative and A is commutative.     

Electron-impact excitation cross-sections for the3 S 0−,3 P 0−, and3 D 0-States of a ruthenium atom

The excitation cross-sections of transitions of a ruthenium atom from the³ S ⁰−,³ P ⁰−, and³ D ⁰-levels are measured by the method of extended crossed beams. Based on the results of measurements, the excitation cross-sections of the states are calculated (ignoring cascade contribution). Moscow Power Engineering Institute, 14, Krasnokazarmennaya St., Moscow, E-250, 111250, Russia. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 65, No. 1, pp. 9–13, January–February, 1998.