On the Indecomposable Modules of Uq（sl（2）） Constructed via Ore-extension

Let A be a subalgebra of Uq (sl(2)) generated by K, K-1 and F and Aδ be a subalgebra of Uq (sl(2)) generated by K, K-1 (and also Fd if q is a primitive d-th root of unity with d an odd number). Given an Aδ -module M, a Uq (sl(2))-module AAδ M is constructed via the iterated Ore extension of Uq (sl(2)) in a unified framework for any q. Then all the submodules of AAδ M are determined for a fixed finite-dimensional indecomposable Aδ -module M . It turns out that for some indecomposable Aδ -module M , the Uq (sl(2))-module AAδ M is indecomposable, which is not in the BGG-categories Oq associated with quantum groups in general.     

Orthosymplectic Quantum Function Superalgebras OSPq（2l＋ 1｜2n）

By the R-matrix of orthosymplectic quantum superalgebra U _q (osp(2l+1|2n)) in the vector representation, we establish the corresponding quantum Hopf superalgebra OSP _q (2l + 1|2n). Furthermore, it is shown that OSP _q (2l + 1|2n) is coquasitriangular.     

A Class of Finite-Dimensional Representations of U_q（sl_2）

In order to study a class of finite-dimensional representations of Uq（sl2）, we deal with the quotient algebra Uq （m, n, b） of quantum group Uq（sl2） with relations Kr=1, Emr=b, Fnr=0 in this paper, where q is a root of unity. The algebra Uq（m, n, b） is decomposed into a direct sum of indecomposable （left） ideals. The structures of indecomposable projective representations and their blocks are determined.     

SOME NEW FAMILIES OF FILTRATION FIVE IN THE STABLE HOMOTOPY OF SPHERES

This study proves a general result on convergence of α2x ∈ ExtA^s＋2.tq＋2q＋1 （Zp, Zp） in the Adams spectral sequence and as a consequence, the study detects some new families in the stable homotopy groups of spheres πtq＋2q-4S which is represented in the Adams spectral sequence by α2fn,α2fn,α2huhmhn ∈ ExtA^5,tq＋2q＋1（Zp,Zp） with tq=p^n＋1q＋2p^nq,2p^n＋1q_P^nq,p^uq＋p^mq＋p^nq,respectively, where α2∈Extα^2,2q＋1（Zp,Zp）,fn∈ExtA^3,p^n＋1q＋2p^nq（Zp,Zp）,fn∈ExtA^3,2p^n＋2q＋p^nq（Zp,Zp）,hn∈ExtA^1,p^nq（Zp,Zp）and p≥5 is a prime,q=2（p=-1）,n≥2.     

On the index of Fredholm pairs of idempotents

Using the technique of block-operators, in this note, we prove that if P and Q are idempotents and （P - Q）^2n＋1 is in the trace class, then （P - Q）^2m＋1 is also in the trace class and tr（P - Q）^2m＋1 = dim（k（P） ∩ k（Q）^⊥） -dim（k（P）^⊥ N k（Q））, for all m ≥ n. Moreover, we prove that dim（k（P）∩ k（Q）^⊥） = dim（k（P）^⊥ ∩k（Q）） if and only if there exists a unitary U such that UP = QU and PU = UQ, where k（T） denotes the range of T. Keywords Fredholm, orthogonal projection, positive operator     

Extensions of quantum enveloping algebras

In this paper, we define a class of extended quantum enveloping algebras U _q (f(K, J)) and some new Hopf algebras, which are certain extensions of quantum enveloping algebras by a Hopf algebra H. This construction generalizes some well-known extensions of quantum enveloping algebras by a Hopf algebra and provides a large of new noncommutative and noncocommutative Hopf algebras.     

高效绿色硫化氢转化制氢技术 太阳能光电催化-化学耦合分解硫化氢制氢研究获突破

<正>2014年4月4日,中国科学院大连化学物理研究所洁净能源国家实验室太阳能研究部李灿院士团队和昆士兰大学纳米材料中心逯高清(Max Lu)、王连洲教授团队合作,在光电催化-化学耦合分解硫化氢研究中取得重要进展,相关研究成果发表在德国《应用化学》(Angew.Chem.Int.Ed.2014,doi:/10.1002/anie.201400571)上,并被评为"hot paper"(热点文章)。     

INITIAL TRACE OF SOLUTIONS FOR A DOUBLY NONLINEAR DEGENERATE PARABOLIC EQUATIONS

In this note, we study the existence of an initial trace of nonnegative solutions for the following problem ut-div(|▽um|p-2▽um)+uq = 0 in QT = Ω× (0, T ). We prove that the initial trace is an outer regular Borel measure, which may not be locally bounded for some values of parameters p, q, and m. We also study the corresponding Cauchy problems with a given generalized Borel measure as initial data.