Dilations of Contraction Cocycles and Cocycle Perturbations of the Translation Group of the Line

The class of contraction cocycles which can be dilated to unitary Markovian cocycles of a translation group S on the straight line is introduced. The class of cocycle perturbations of S by unitary Markovian cocycles W with the property W _t ? I ∈ S ₂ (the Hilbert—Schmidt class) is investigated. The results are applied to perturbations of Kolmogorov flows on hyperfinite factors generated by the algebra of canonical anticommutation relations.     

Construction of some quantum stochastic operator cocycles by the semigroup method

A new method for the construction of Fock-adapted quantum stochastic operator cocycles is outlined, and its use is illustrated by application to a number of examples arising in physics and probability. The construction uses the Trotter-Kato theorem and a recent characterisation of such cocycles in terms of an associated family of contraction semigroups. In celebration of Kalyan Sinha’s sixtieth birthday     

对合导子构造的3-李双代数与3-Pre-李代数

研究具有对合导子的3-李代数的结构,证明了具有对合导子的m-维3-李代数A存在相容的3-Pre-李代数,且在2m-维半直积3-李代数A■_(ad~*)A~*上存在局部上循环3-李双代数结构.利用对合导子构造了3-李代数A■_(ad~*)A~*上的3-李Yang-Baxter方程的解和一类3-Pre-李代数,并构造了8-维和10-维局部上循环3-李双代数.     

Cocycle Twisting of E(n)-Module Algebras and Applications to the Brauer Group

We classify the orbits of coquasi-triangular structures for the Hopf algebra E(n) under the action of lazy cocycles and the Hopf automorphism group. This is applied to detect subgroups of the Brauer group BQ(k,E(n)) of E(n) that are isomorphic. For any triangular structure R on E(n) we prove that the subgroup BM(k,E(n),R) of BQ(k,E(n)) arising from R is isomorphic to a direct product of BW(k), the Brauer-Wall group of the ground field k, and Sym_n(k), the group of n × n symmetric matrices under addition. For a general quasi-triangular structure R on E(n) we construct a split short exact sequence having BM(k,E(n),R⁾ as a middle term and as kernel a central extension of the group of symmetric matrices of order r < n (r depending on R). We finally describe how the image of the Hopf automorphism group inside BQ(k,E(n)) acts on Sym_n (k).     

局部2-上循环

The aim of this paper is to show that every local 2-cocycle of a von Neumann algebra R with coefficients in .Y (a unital dual R-bimodule) is a 2-cocycle.     

Universal R-Matrix for Esoteric Quantum Groups

The universal R-matrix for a class of esoteric (nonstandard) quantum groups q(gl(2N+1)) is constructed as a twisting of the universal R-matrix S of the Drinfeld–Nimbo quantum algebras. The main part of the twisting cocycle is chosen to be the canonical element of an appropriate pair of separated Hopf subalgebras (quantized Borel's (N) q (gl(2N+1))), providing the factorization property of . As a result, the esoteric quantum group generators can be expressed in terms of Drinfeld and Jimbo.     

Bicross-Product Structure of Affine Quantum Groups

We show that the affine quantum group is isomorphic to a bicross-product central extension of the quantum loop group by a quantum cocycle in R-matrix form.     

Impulsive non‐autonomous dynamical systems and impulsive cocycle attractors

In this work, we define the notions of ‘impulsive non‐autonomous dynamical systems’ and ‘impulsive cocycle attractors’. Such notions generalize (we will see that not in the most direct way) the notions of autonomous dynamical systems and impulsive global attractors in the current published literature. We also establish conditions to ensure the existence of an impulsive cocycle attractor for a given impulsive non‐autonomous dynamical system, which are analogous to the continuous case. Moreover, we prove the existence of such attractor for a non‐autonomous 2D Navier–Stokes equation with impulses, using energy estimates. Copyright © 2016 John Wiley & Sons, Ltd.     

Cocyclic Codes of Length 40

There are 5 groups of order 20. This paper reports on the search for binary self-dual codes of length 40, cocyclic over any one of the first four groups, using cocyclic Hadamard matrices and the [I, A] construction. The fifth group is not investigated here. A total of 28 classes of extremal cocyclic self-dual codes were found—27 of these are doubly-even and one singly-even. The majority of these classes arise from the dihedral-cocyclic Hadamard matrices. There is also a class of dihedral-cocyclic Hadamard matrices which gives a large collection of [40, 20] codes with only one codeword of length 4.     

A Crossed Module Representing the Godbillon–Vey Cocycle

We exhibit crossed modules of Lie algebras (i.e. certain four-term exact sequences) corresponding to the Godbillon–Vey generator for the Lie algebras of formal vector fields in one variable, of vector fields on the circle, of differentiable vector fields of holomorphic type and of holomorphic vector fields on a punctured Riemann surface.