共查询到20条相似文献,搜索用时 31 毫秒
1.
In this paper we study the representation theory for certain “half lattice vertex algebras.” In particular we construct a large class of irreducible modules for these vertex algebras. We also discuss how the representation theory of these vertex algebras are related to the representation theory of some associative algebras. 相似文献
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We present a framework for extending Stone's representation theorem for distributive lattices to representation theorems for distributive lattices with operators. We proceed by introducing the definition of algebraic theory of operators over distributive lattices. Each such theory induces a functor on the category of distributive lattices such that its algebras are exactly the distributive lattices with operators in the original theory. We characterize the topological counterpart of these algebras in terms of suitable coalgebras on spectral spaces. We work out some of these coalgebraic representations, including a new representation theorem for distributive lattices with monotone operators. 相似文献
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Jia Huang 《Annals of Combinatorics》2016,20(4):831-868
A 0-Hecke algebra is a deformation of the group algebra of a Coxeter group. Based on work of Norton and Krob-Thibon, we introduce a tableau approach to the representation theory of 0-Hecke algebras of type A, which resembles the classic approach to the representation theory of symmetric groups by Young tableaux and tabloids. We extend this approach to types B and D, and obtain a correspondence between the representation theory of 0-Hecke algebras of types B and D and quasisymmetric functions and noncommutative symmetric functions of types B and D. Other applications are also provided. 相似文献
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代数表示论是本世纪七十年代初兴起的代数学的一个新的分支。它的基本内容是研究一个Artin代数上的模范畴。由于各国代数学家的共同努力,这一理论于最近二十年代有了异常迅猛的发展并逐步趋于完善。本文介绍了代数表示论的理论基础;几乎可裂序列;箭图和赋值箭图的表示;Coxeter函子;AR-箭图的覆盖及代数的Galois覆盖。并简单介绍了在代数表示论中普遍应用的工具:Tilt理论,以及著名的Dpozg定理证 相似文献
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Inaba Hiroshi; Abdursul Rixat; Takahashi Satoru 《IMA Journal of Mathematical Control and Information》2003,20(1):21-35
This paper develops a new representation theory of multivariabletime-invariant linear systems based on the well-known coprimefactorizations of their transfer matrices. This representationfully uses the algebraic structure of coprime factorizations,and hence has a number of advantages for describing variousproperties of linear systems in simpler and/or more compactforms than the usual transfer matrix representation. In theframework of this new representation theory, various stabilityand stabilizability properties of linear systems are characterizedand finally a simultaneous stabilization problem for a givenset of linear systems is examined. 相似文献
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Deng-Feng Li 《Fuzzy Optimization and Decision Making》2011,10(1):45-58
The Atanassov’s intuitionistic fuzzy (IF) set theory has become a popular topic of investigation in the fuzzy set community.
However, there is less investigation on the representation of level sets and extension principles for interval-valued intuitionistic
fuzzy (IVIF) sets as well as algebraic operations. In this paper, firstly the representation theorem of IVIF sets is proposed
by using the concept of level sets. Then, the extension principles of IVIF sets are developed based on the representation
theorem. Finally, the addition, subtraction, multiplication and division operations over IVIF sets are defined based on the
extension principle. The representation theorem and extension principles as well as algebraic operations form an important
part of Atanassov’s IF set theory. 相似文献
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(1)本文摒弃了传统的四元数理论,建立了Dirac-Pauli表象的复变函数理论,从而使多元多维问题成为较简单的问题;(2)本文用Dirac-Pauli表象的复变函数理论,简化了不可压缩粘流动力学的Navier-Stokes方程和等熵气体动力学方程组,使作为流体力学中心问题的上述两类方程组化归为只有一个复未知量的非线性方程.是故易有太极,是生两仪;两仪生四象,四象生八卦.——《易传·系辞上》. 相似文献
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Aslak Bakke Buan Robert J. Marsh Idun Reiten 《Transactions of the American Mathematical Society》2007,359(1):323-332
We introduce a new class of algebras, which we call cluster-tilted. They are by definition the endomorphism algebras of tilting objects in a cluster category. We show that their representation theory is very close to the representation theory of hereditary algebras. As an application of this, we prove a generalised version of so-called APR-tilting.
10.
Dag Tjøstheim 《Journal of multivariate analysis》1975,5(3):314-321
It is shown that the representation theory of a multivariate, purely nondeterministic, wide sense stationary generalized process can be reduced to a study of some isomorphism results established for commutation relations occurring in quantum mechanics. Using this simplification a multiplicity theory is developed. The time domain and spectral representation of the process are investigated in this context, and the concept of a generalized innovations process is introduced. 相似文献
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Summary A customary representation formula for periodic spline interpolants contains redundance which, however, can be eliminated by a transcendent method. We use an elementary indentity for the generalized Euler-Frobenius-polynomials, which seems to be unknown until now, in order to derive the theory by purely algebraic arguments. The general cardinal spline interpolation theory can be obtained from the periodic case by a simple approach to the limit. Our representation has minimum condition for odd/even degree if the interpolation points are the lattice (mid-)points. We evaluate the corresponding condition numbers and give an asymptotic representation for them. 相似文献
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Analysis of function spaces and special functions are closely related to the representation theory of Lie groups. We explain here the connection between the Laguerre functions, the Laguerre polynomials, and the Meixner–Pollacyck polynomials on the one side, and highest weight representations of Hermitian Lie groups on the other side. The representation theory is used to derive differential equations and recursion relations satisfied by those special functions. 相似文献
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Tammo tom Dieck 《manuscripta mathematica》1978,26(1-2):179-200
We are concerned with the homotopy theory of group representations and its relation to character theory and the theory of the Burnside ring. We combine the methods of tom Dieck — Petrie [4] and torn Dieck [3] to show that the canonical map from the J-group jO(G), a subquotient of the representation ring RO(G), into the Picard group of the rational representation ring is injective for p-groups G. Moreover we compute the order of the cokernel of this map. We show that the Picard group of the rational representation ring is a direct summand in the Picard group of the Burnside ring. Finally we compute the Picard groups if G is abelian and indicate a computation for general G. 相似文献
14.
Split preorders are preordering relations on a domain whose composition is defined in a particular way by splitting the domain into two disjoint subsets. These relations and the associated composition arise in categorial proof theory in connection with coherence theorems. Here split preorders are represented isomorphically in the category whose arrows are binary relations and whose composition is defined in the usual way. This representation is related to a classical result of representation theory due to Richard Brauer. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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For each finite subgroup G of SLn(C), we introduce the generalized Cartan matrix AG in view of McKay correspondence from the fusion rule of its natural representation. Using group theory, we show that the generalized Cartan matrices have similar favorable properties such as positive semi- definiteness as in the classical case of affine Cartan matrices. The complete McKay quivers for SL3 (C) are explicitly described and classified based on representation theory. 相似文献
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Mathematische Zeitschrift - Diagram algebras, in particular Brauer algebras, Birman–Murakami-Wenzl algebras and partition algebras, are used in representation theory and invariant theory of... 相似文献
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《Quaestiones Mathematicae》2013,36(2):215-232
Abstract Graded Artin algebras whose category of graded modules is locally of finite representation type are introduced. The representation theory of such algebras is studied. In the hereditary case and in the stably equivalent to hereditary case, such algebras are classified. 相似文献
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Norman E. Hurt 《Results in Mathematics》1993,23(1-2):55-120
The article reviews the interrelationship of periodic orbit theory and the Selberg trace formula. Examples from recent work on quantization of chaos are surveyed. The review emphasizes the development in terms of Lie group representation theory and differential geometry. Finally, the formal connections to string theory are discussed. 相似文献
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该文使用投影算子方法研究任意除环上矩阵的广义逆, 建立了具有指定值域和零空间的{2} 逆的刻划和表示理论. 作为应用, 获得了带有对合函数的Moore Penrose逆, 群逆和Dra zin逆的一些新的表式. 相似文献