Classification of ℤ2-graded modules of intermediate series over a Block-type Lie algebra

2015 ◽  
Vol 17 (05) ◽  
pp. 1550059
Author(s):  
Yucai Su ◽  
Xiaoqing Yue

Let [Formula: see text] be the Lie algebra of Block type with basis {Li,j | i,j ∈ ℤ} and relations [Li,j, Lk,l] = ((j + 1)k - (l + 1)i)Li+k,j+l. Since [Formula: see text] is ℤ2-graded, it is natural to study ℤ2-graded modules over [Formula: see text]. In this paper, ℤ2-graded [Formula: see text]-modules of the intermediate series are classified.

2015 ◽  
Vol 22 (03) ◽  
pp. 367-382 ◽  
Author(s):  
Ming Gao ◽  
Ying Xu ◽  
Xiaoqing Yue

Let L be a Lie algebra of Block type over ℂ with basis {Lα,i | α,i ∈ ℤ} and brackets [Lα,i,Lβ,j]=(β(i+1)-α(j+1)) Lα+β,i+j. In this paper, we first construct a formal distribution Lie algebra of L. Then we decide its conformal algebra B with ℂ[∂]-basis {Lα(w) | α ∈ ℤ} and λ-brackets [Lα(w)λ Lβ(w)]= (α∂+(α+β)λ) Lα+β(w). Finally, we give a classification of free intermediate series B-modules.


2010 ◽  
Vol 17 (02) ◽  
pp. 247-256
Author(s):  
Yina Wu ◽  
Weiqiang Lin

In this paper, we complete the classification of Z-graded modules of the intermediate series over a q-analog Virasoro-like algebra L. We first construct four classes of irreducible Z-graded L-modules of the intermediate series. Then we prove that any Z-graded L-module of the intermediate series must be one of the modules constructed by us, or a direct sum of some trivial L-modules.


2020 ◽  
Vol 27 (02) ◽  
pp. 343-360 ◽  
Author(s):  
Hengyun Yang ◽  
Ying Xu ◽  
Jiancai Sun

The topological N = 2 superconformal algebra was introduced by Dijkgraaf, Verlinde and Verlinde as the symmetry algebra of topological strings at d < 1. We give a classification of irreducible 𝕫 × 𝕫-graded modules of the intermediate series over this infinite-dimensional Lie superalgebra.


2013 ◽  
Vol 393 ◽  
pp. 71-78 ◽  
Author(s):  
Yucai Su ◽  
Chunguang Xia ◽  
Ying Xu
Keyword(s):  

2013 ◽  
Vol 20 (02) ◽  
pp. 181-196 ◽  
Author(s):  
Weiqiang Lin ◽  
Yucai Su

In this paper, we consider the classification of irreducible Z- and Z2-graded modules with finite-dimensional homogeneous subspaces over the Virasoro-like algebra. We prove that such a module is a uniformly bounded module or a generalized highest weight module. Then we determine all generalized highest weight quasi-finite irreducible modules. As a consequence, we determine all the modules with nonzero center. Finally, we prove that there does not exist any non-trivial Z-graded module of intermediate series.


2019 ◽  
Vol 18 (01) ◽  
pp. 1950002 ◽  
Author(s):  
Xiangqian Guo ◽  
Genqiang Liu

In this paper, we studied the jet modules for the centerless Virasoro-like algebra which is the Lie algebra of the Lie group of the area-preserving diffeomorphisms of a [Formula: see text]-torus. The jet modules are certain natural modules over the Lie algebra of semi-direct product of the centerless Virasoro-like algebra and the Laurent polynomial algebra in two variables. We reduce the irreducible jet modules to the finite-dimensional irreducible modules over some infinite-dimensional Lie algebra and then characterize the irreducible jet modules with irreducible finite dimensional modules over [Formula: see text]. To determine the indecomposable jet modules, we use the technique of polynomial modules in the sense of [Irreducible representations for toroidal Lie algebras, J. Algebras 221 (1999) 188–231; Weight modules over exp-polynomial Lie algebras, J. Pure Appl. Algebra 191 (2004) 23–42]. Consequently, indecomposable jet modules are described using modules over the algebra [Formula: see text], which is the “positive part” of a Block type algebra studied first by [Some infinite-dimensional simple Lie algebras in characteristic [Formula: see text] related to those of Block, J. Pure Appl. Algebra 127(2) (1998) 153–165] and recently by [A [Formula: see text]-graded generalization of the Witt-algebra, preprint; Classification of simple Lie algebras on a lattice, Proc. London Math. Soc. 106(3) (2013) 508–564]).


Author(s):  
С.А. Демидов

Рассматриваются возможности применения системы машин модульно-блочного типа в перспективных технологиях лесосечных работ, а также проблемы машинного парка лесозаготовительных предприятий России. Цель исследования - изучение структуры и особенностей эксплуатации системы лесных машин модульно блочного типа в современных условиях лесозаготовок с перспективой применения на ближайшее будущее. Для улучшения технологии проведения лесосечных работ и повышения экономической эффективности лесопромышленного комплекса предлагается провести ряд важных технических и технологических изменений. Одним из решений проблемы по улучшению эффективности работы является разработка и внедрение комплекса лесных машин, основанного на принципе эксплуатационной модульности. Это будет гарантировать технологическую гибкость производства, предоставит высокую производительность и обеспечит совместимость с окружающей средой. Приведен принцип устройства машин модульно-блочного типа с разделением функций между транспортными и технологическими модулями. Представлены графически классификация модулей по их назначению и концепция компоновки системы машин модульно-блочного типа, а также главный модуль (энергетический) и несколько технологических модулей, способных выполнять различные технологические операции в зависимости от условий и технологии производства. Как показал анализ рынка, наиболее перспективным направлением по улучшению механизации лесного парка машин является создание комплекса модульно-блочных машин на базе колесного трактора, оснащенных гидрообъемными передачами. Это делает конструкцию машины более гибкой и мобильной. Принцип формирования и работы модульной системы машин с многофункциональным технологическим оборудованием рассматривается в качестве перспективного направления по улучшению лесозаготовительного процесса. The article deals with the prospects for the use of machines modular block type in the advanced technology logging activities, as well as the machinery problems of logging enterprises in Russia. The research objective. The study of the structure and operating characteristics of a system of forest modular block type machines in current conditions with the prospect of their application in the nearest future. It is necessary that a number of important technical and technological changes should be made to improve the technology of logging operations and increase the economic efficiency of timber industry complex. One of the solutions to improve work efficiency is the development and introduction of forest machines based on the principle of operational modularity. It will ensure the flexibility of the production process, provide high work efficiency and, what counts, will be environmentally friendly. The article gives the description of the principle of the machine module block type, as well as the functions and how they are divided between the two modules. There are two pictures in the article. The first picture gives the classification of modules according to their application. The second picture shows the principle of arrangement of modular machine-block type. Both the main energetic module and some technological modules capable of performing processing steps depending on the conditions and production technology are presented. According to the market analysis that shows that the most promising direction to improve the mechanization of forest machinery is to create a complex modular block machines on the base of a wheeled tractor equipped with hydrostatic transmission. It will make the machine design more flexible and mobile. The principle of formation and operation of the modular system with multi-function machines process equipment is considered as a promising direction for improvement of the process of logging.


2016 ◽  
Vol 31 (17) ◽  
pp. 1650102 ◽  
Author(s):  
Tahir Hussain ◽  
Sumaira Saleem Akhtar ◽  
Ashfaque H. Bokhari ◽  
Suhail Khan

In this paper, we present a complete classification of Bianchi type II spacetime according to Ricci inheritance collineations (RICs). The RICs are classified considering cases when the Ricci tensor is both degenerate as well as non-degenerate. In case of non-degenerate Ricci tensor, it is found that Bianchi type II spacetime admits 4-, 5-, 6- or 7-dimensional Lie algebra of RICs. In the case when the Ricci tensor is degenerate, majority cases give rise to infinitely many RICs, while remaining cases admit finite RICs given by 4, 5 or 6.


2016 ◽  
Vol 27 (06) ◽  
pp. 1650057 ◽  
Author(s):  
Haibo Chen ◽  
Jianzhi Han ◽  
Yucai Su ◽  
Ying Xu

In this paper, we introduce two kinds of Lie conformal algebras, associated with the loop Schrödinger–Virasoro Lie algebra and the extended loop Schrödinger–Virasoro Lie algebra, respectively. The conformal derivations, the second cohomology groups of these two conformal algebras are completely determined. And nontrivial free conformal modules of rank one and [Formula: see text]-graded free intermediate series modules over these two conformal algebras are also classified in the present paper.


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