Hopf group-coalgebras

We study algebraic properties of Hopf group-coalgebras, recently introduced by Turaev. We show the existence of integrals and traces for such coalgebras, and we generalize the main properties of quasitriangular and ribbon Hopf algebras to the setting of Hopf group-coalgebras.     

A time- and spaceadaptive algorithm for the linear time-dependent Schrödinger equation

Summary. We prove an a posteriori error estimate for the linear time-dependent Schr?dinger equation in . From this, we derive a residual based local error estimator that allows us to adjust the mesh and the time step size in order to obtain a numerical solution with a prescribed accuracy. As a special feature, the error estimator controls localization and size of the finite computational domain in each time step. An algorithm is described to compute this solution and numerical results in one space dimension are included. Received March 17, 1995     

Yangians: Their representations and characters

The finite-dimensional irreducible representations of the Yangian of sl₂ are parametrized by their highest weights, which are monic polynomials in one variable. In this paper, we give a formula for the character of such a representation which depends only on its highest weight, and is an analogue of the classical Weyl character formula.     

What must and what need not be contained in a graph of uncountable chromatic number?

We investigate the following problem: What countable graphs must a graph of uncountable chromatic number contain? We define two graphsΓ andΔ which are very similar and we show thatΓ is contained in every graph of uncountable chromatic number, whileΔ is (consistently) not.     

Rates of convergence of random walk on distance regular graphs

When run on any non-bipartite q-distance regular graph from a family containing graphs of arbitrarily large diameter d, we show that d steps are necessary and sufficient to drive simple random walk to the uniform distribution in total variation distance, and that a sharp cutoff phenomenon occurs. For most examples, we determine the set on which the variation distance is achieved, and the precise rate at which it decays. The upper bound argument uses spectral methods – combining the usual Cauchy-Schwarz bound on variation distance with a bound on the tail probability of a first-hitting time, derived from its generating function. Received: 2 April 1997 / Revised version: 10 May 1998     

Free products of kω-topological groups with normal amalgamation

It is shown in this paper that if A is a closed normal subgroup of k_ω-topological groups G and H, then the free product of G and H with A amalgamated, G1_AH, exists, is Hausdorff and indeed a k_ω-group.