Solutions of the Yang–Baxter equations on quadratic Lie groups: The case of oscillator groups

A Lie group is called quadratic if it carries a bi-invariant semi-Riemannian metric. Oscillator Lie groups constitute a subclass of the class of quadratic Lie groups. In this paper, we determine the Lie bialgebra structures and the solutions of the classical Yang–Baxter equation on a generic class of oscillator Lie algebras. Moreover, we show that any solution of the generalized classical Yang–Baxter equation (resp. classical Yang–Baxter equation) on a quadratic Lie group determines a left invariant locally symmetric (resp. flat) semi-Riemannian metric on the corresponding dual Lie groups.     

Cross sections for (d–t) neutron interaction with germanium isotopes

The cross sections for (n,x)$(n,x)$ reactions with Ge isotopes were measured at (d–t) neutron energies around 14 MeV with the activation technique using metal discs of natural composition. Calculations of detector efficiency, incident neutron spectrum and correction factors were performed with the Monte Carlo technique (MCNP4C code). Cross sections data are presented for ⁷⁰Ge(n,2n$n,2n$)⁶⁹Ge, ⁷⁴Ge(n,α$n,\alpha$)^71mZn, ⁷⁶Ge(n,2n$n,2n$)^75(m + g)Ge, ⁷⁰Ge(n,p$n,p$)⁷⁰Ga and ⁷²Ge(n,2n$n,2n$)^71gGe reactions. The cross section results for ⁷²Ge(n,2n$n,2n$)^71gGe reaction were reported for the first time. Some other cross sections were obtained with higher precision, including the ⁷⁰Ge(n,p$n,p$)⁷⁰Ga reaction. Theoretical calculations of excitation functions were performed with the TALYS-1.0 code and compared with the experimental cross section values. Data were included in the EXFOR database.     

The Gelfand-Kirillov conjecture and Gelfand-Tsetlin modules for finite W-algebras

We address two problems with the structure and representation theory of finite W-algebras associated with general linear Lie algebras. Finite W-algebras can be defined using either Kostant's Whittaker modules or a quantum Hamiltonian reduction. Our first main result is a proof of the Gelfand-Kirillov conjecture for the skew fields of fractions of finite W-algebras. The second main result is a parameterization of finite families of irreducible Gelfand-Tsetlin modules using Gelfand-Tsetlin subalgebra. As a corollary, we obtain a complete classification of generic irreducible Gelfand-Tsetlin modules for finite W-algebras.     

The Popescu-Gabriel theorem for triangulated categories

The Popescu-Gabriel theorem states that each Grothendieck abelian category is a localization of a module category. In this paper, we prove an analogue where Grothendieck abelian categories are replaced by triangulated categories which are well generated (in the sense of Neeman) and algebraic (in the sense of Keller). The role of module categories is played by derived categories of small differential graded categories. An analogous result for topological triangulated categories has recently been obtained by A. Heider.     

Polynomial invariants for a semisimple and cosemisimple Hopf algebra of finite dimension

We introduce new polynomial invariants of a finite-dimensional semisimple and cosemisimple Hopf algebra A over a field by using the braiding structures of A. The coefficients of polynomial invariants are integers if is a finite Galois extension of Q, and A is a scalar extension of some finite-dimensional semisimple Hopf algebra over Q. Furthermore, we show that our polynomial invariants are indeed tensor invariants of the representation category of A, and recognize the difference between the representation category and the representation ring of A. Actually, by computing and comparing polynomial invariants, we find new examples of pairs of Hopf algebras whose representation rings are isomorphic, but whose representation categories are distinct.     

Iyama’s finiteness theorem via strongly quasi-hereditary algebras

Let Λ be an artin algebra and X a finitely generated Λ-module. Iyama has shown that there exists a module Y such that the endomorphism ring Γ of X⊕Y is quasi-hereditary, with a heredity chain of length n, and that the global dimension of Γ is bounded by this n. In general, one only knows that a quasi-hereditary algebra with a heredity chain of length n must have global dimension at most 2n−2. We want to show that Iyama’s better bound is related to the fact that the ring Γ he constructs is not only quasi-hereditary, but even left strongly quasi-hereditary. By definition, the left strongly quasi-hereditary algebras are the quasi-hereditary algebras with all standard left modules of projective dimension at most 1.     

Strong commutativity preserving maps in prime rings with involution

Let A be a prime ring of characteristic not 2, with center Z(A) and with involution *. Let S be the set of symmetric elements of A. Suppose that f:S→A is an additive map such that [f(x),f(y)]=[x,y] for all x,y∈S. Then unless A is an order in a 4-dimensional central simple algebra, there exists an additive map μ:S→Z(A) such that f(x)=x+μ(x) for all x∈S or f(x)=-x+μ(x) for all x∈S.     

Inhomogeneous quantum groups and their quantized universal enveloping algebras

The quantum group IGL _q (N), the inhomogenization of GL _q (N), is formulated with -matrices. Theq-deformed universal enveloping algebra is constructed as the algebra of regular functionals in this formulation and contains the partial derivatives of the covariant differential calculus on the quantum space.     

Tungsten doped mesoporous SBA‐16 as novel heterogeneous catalysts for oxidation of cyclopentene to glutaric acid

Novel heterogeneous tungsten species in mesoporous silica SBA‐16 catalysts based on ship‐in‐a‐bottle methodology are originally reported for oxidizing cyclopentene (CPE) to glutaric acid (GAC) using hydrogen peroxide (H₂O₂). For all W‐SBA‐16 catalysts, isolated tungsten species and octahedrally coordinated tungsten oxide species are observed while WO₃ crystallites are detected for the W‐SBA‐16 catalysts with Si/ W = 5, 10, and 20. The specific surface areas and the corresponding total pore volumes decrease significantly as increasing amounts of tungsten incorporated into the pores of SBA‐16. Using tungsten‐substituted mesoporous SBA‐16 heterogeneous catalysts, high yield of GAC (55%) is achieved with low tungsten loading (for Si/W = 30, ~13 wt%) for oxidation of CPE. The W‐SBA‐16 catalysts with Si/W = 30 can be reused five times without dramatic deactivation. In fact, low catalytic activity provided by bulk WO₃ implies that the highly distributed tungsten species in SBA‐16 and the steric confinement effect of SBA‐16 are key elements for the outstanding catalytic performance.     

N—甲基异靛蓝在不同溶剂中的^1H—NMR研究

用选择照射方法研究了N-甲基异靛蓝(isoindigatin)在(CD_3)_2CO、CDCl_3、DMSO-d_6溶剂中及重水交换后的~1H NMR谱。得到了化学环境极为类似的两芳环质子在不同溶剂中的NMR谱线归属和偶合常数。