Twist积和Twist余积Hopf代数

设H,A是两个Hopf代数,构造了twist积A#_σH和twist余积A#~(?)H,证明了文[1]中的double twist和S.Majid构造的Bicrossproduct结构以及通常的smash积都是A#_σH的一种特殊情况;文[2,3]中的twist Hopf代数以及通常的smash余积是A#~(?)H的特殊情况,最后讨论了A#~(?)H上的拟三角结构.     

(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.     

Majid double双积的一种广义型（英文）

设H为双代数.σ:HH→A为线性映射,其中A为左H余模余代数,且是带有左H-弱作用的代数.τ:HB→B为线性映射,其中B为右H余模余代数,且是带有右H-弱作用的代数.本文给出双边交叉积A#_σH_τ#B和双边smash余积构成双代数的充要条件.这一结构包括了著名的Radford双积(见[J.Algebra,1985,92(2):322-347]),Majid double双积(见[Math.Proc.Cambridge Philos.Soc.,1999,125(1):151-192]),以及王栓宏、焦争鸣和赵文正定义的交叉积(见[Comm.Algebra,1998,26(4):1293-1303]).     

扭曲的自对偶Hopf代数

从两种重要的结构crossed积代数和扭曲Smash余积余代数出发,构造了一类新的Hopf代数R(?)K#_σH,并讨论它成为自对偶Hopf代数的条件.     

Hom-弱Hopf代数上的Hom-smash余积

本文研究了在Hom-Hopf代数上引入Hom-弱Hopf代数的问题.利用建立弱左H-Hom-余模双代数的方法,获得了Hom-smash余积的代数结构,并证明了Hom-smash余积是Hom-余代数和Hom-弱Hopf代数,推广了由Molnar定义的smash余积Hopf代数.     

模余代数和Morita-Takeuchi关系

H是Hopf代数,C是H-模余代数.首先利用余积分的概念,诱导C的右H-余模结构,并构造了smash余积余代数C×H,使C×H作为余代数同构于C H.然后,由C的右H-余模结构诱导C的左H0-模结构,令C=C/KerεH0C,则C×H与C有Morita-Takeuchi关系.     

单的模代数及其稳定化子

研究了有限维Hopf代数H与其单的模代数A的smash积的结构.通过给出A的反代数与其极小左理想的稳定化子的结构,证明了H与A的smash积与某个代数上的全矩阵代数是代数同构的,推广了以往的结果.     

辫子monoidal范畴中的Smash余积和辫子群

给出了辫子monoidal范畴C中的smash余积结构及使它成为Hopf代数或辫子Hopf代数的条件。在重要的范畴^HM中证明了一类辫子群与任何Hopf代数作smash余积是某个Hopf代数的变形,为变形理论提供了方法。对2-余循环σ构造了H_σ,当H为变换时,证明它同构于H^σ经变形后的辫子群(H^σ)=A(H^σ,id,H^σ)。特别地,由某些杨-Baxter方程的解可构造出辫子群。     

偶交叉双积Hopf代数B_T_RH的构造

本文给出了DoiY．构造的偶交叉积BT■H的代数结构与ReshetikhimN．构造的双代数B■RH的余代数结构在张量空间B■H上构成双代数（记为Bτ■RH）的充要条件,利用此结论具体构造了一个有趣的例子B4■KZ2;证明了当B,H均为Hopf．代数时Bτ■RH也为Hopf代数,最后给出这类双代数的映射刻划。     

偶交叉双积Hopf代数B_T_RH的构造

本文给出了DoiY．构造的偶交叉积BT■H的代数结构与ReshetikhimN．构造的双代数B■RH的余代数结构在张量空间B■H上构成双代数（记为Bτ■RH）的充要条件,利用此结论具体构造了一个有趣的例子B4■KZ2;证明了当B,H均为Hopf．代数时Bτ■RH也为Hopf代数,最后给出这类双代数的映射刻划。     

Twist of deformation characteristics

Consider a regular surface in three-dimensional euclidean space subject to deformation. The difference between the torsion of a curve L on the original surface and the torsion of the corresponding curve on the isometric deformed surface at points corresponding by the isometry is called the twist of L. A formula is introduced expressing the twist of characteristics of hyperbolic deformation of a surface in terms of its gaussian flexion.Translated from Matematicheskie Zametki, Vol. 9, No. 3, pp. 233–238, March, 1971.     

Twist Functors and D-Branes

We discuss a categorical approach to the investigation of topological D-branes. Twist functors and their induced action on the cohomology ring of a manifold are studied. A nontrivial spherical object of the derived category of coherent sheaves of a reduced plane singular curve of degree 3 is constructed.__________Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 1, pp. 18–31, January, 2005.     

Extremal Projector and Dynamical Twist

We describe a relation between the dynamical twist J() and the extremal projector for simple Lie algebras. This correspondence finds two obvious applications: first, the solution of the Arnaudon–Buffenoir–Ragoucy–Roche equation can be obtained from the known multiplicative expression for the extremal projector; second, the structure constants are determined by the matrix coefficients of the dynamical twist.     

Twist points of planar domains

We establish a potential theoretic approach to the study of twist points in the boundary of simply connected planar domains.

     

Chaotic Dynamics of Monotone Twist Maps

For a monotone twist map,under certain non-degenerate condition,we showed the existence of infinitely many homoclinic and heteroclinic orbits between two periodic neighboring minimal orbits with the same rotation number,which indicates chaotic dynamics.Our results also apply to geodesics of smooth Riemannian metrics on the two-dimension torus.     

Twist star products and Morita equivalence

We present a simple no-go theorem for the existence of a deformation quantization of a homogeneous space M induced by a Drinfel'd twist: we argue that equivariant line bundles on M with non-trivial Chern class and symplectic twist star products cannot both exist on the same manifold M. This implies, for example, that there is no symplectic star product on the projective space ${\mathbb{CP}}^{n?1}$ induced by a twist based on $U({\mathfrak{gl}}_n(\mathbb{C}))?h?$ or any sub-bialgebra, for every $n\ge 2$.     

Moser扭转定理在Lagrange稳定性中的应用

本文利用Moser扭转定理证明了一类Duffing方程x″ 9(x)=e(t)的Lagrange稳定性，其中e(t)以1为周期，9：R→R具有下列性质：当x≥d0时，9(x)是超线性的；当x≤-d0时，9(x)是次线性的，其中d0是一正常数．