B-Construction and C-Construction

B-construction is a way of obtaining a graded algebra from the triple consisting of an additive category, an object, and an autoequivalence, while C-construction is a way of obtaining an algebra (without unity) from the pair consisting of an additive category and a set of objects. In this article, we study and compare three important classes of algebras in noncommutative algebraic geometry and representation theory of finite dimensional algebras, namely, quantum polynomial algebras, preprojetive algebras and trivial extensions, via these constructions.     

Leonard Pairs and Leonard Triples of q-Racah Type from the Quantum Algebra U q (sl 2)

In this article, we describe the construction of Leonard pairs and Leonard triples that have q-Racah type from U _q (sl ₂)-modules by using equitable generators of U _q (sl ₂). Our result solves an open problem proposed by Terwilliger.     

Graded Clifford Algebras of Prime Global Dimension with an Action of H p

In this article, we study graded Clifford algebras with a gradation preserving action of automorphisms given by H _p , the Heisenberg group of order p ³ with p prime. After reviewing results in dimensions 3 and 4, we will determine the graded Clifford algebras that are AS-regular algebras of global dimension 5 and generalize certain results to arbitrary dimension p.     

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.     

Two-Parameter Analogs of the Heisenberg Enveloping Algebra

One-parameter analogs of the Heisenberg enveloping algebra were studied previously by Kirkman and Small. They demonstrated how one may obtain Hayashi's analog of the Weyl algebra as a primitive factor of this algebra. We consider various two-parameter versions of this problem. Of particular interest is the case when the parameters are dependent. Our study allows us to consider the representation theory of a two-parameter version of the Virasoro enveloping algebra.     

Structure of Quantum Doubles of Finite Clifford Monoids

Abstract

In this paper, over a field k, we give the structure theorem of the quantum double of a finite Clifford monoid through bicrossed products and quantum doubles of groups. By this result, it is shown that the quantum double of a finite Clifford monoid is semisimple (resp. von Neumann regular) if and only if the semigroup is a finite group and the characteristic p of k does not divide the order of this group.     

一维稳态量子Navier-Stokes方程组古典解的唯一性

文[9]得到了一维稳态量子Navier-Stokes方程组古典解的存在性,本文在某些条件下利用一些不等式技巧继续证明了其解的唯一性.     

Effect of a buffer layer between the shell and ligand on the optical properties of an exciton and biexciton in type-II quantum dot nanocrystals

In this study, we have investigated the effect of the buffer layers on the electronic and optical properties of an exciton (X) and a biexciton (XX) in a type-II CdTe/CdSe quantum dot nanocrystal. In an experimental study, it has been reported that when a CdTe/CdSe quantum dot nanocrystal is coated by a ZnTe material as a buffer layer, the photoluminescence quantum yield is growing from 4 to 20%. We have confirmed theoretically this improvement and extended the calculations to an XX structure. In the calculations, two different semiconductor materials, CdS and ZnTe, have been considered for the buffer layer. We have theoretically shown that the buffer layer causes an increase in the radiative oscillator strength of both X and XX. When the ZnTe is used as the buffer layer, the oscillator strength becomes stronger when compared to CdSe buffer material because of higher conduction band offset between CdSe and ZnTe.