共查询到20条相似文献,搜索用时 15 毫秒
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Victor G. Kac 《Advances in Mathematics》2008,217(6):2485-2562
We extend classical results of Kostant et al. on multiplets of representations of finite-dimensional Lie algebras and on the cubic Dirac operator to the setting of affine Lie algebras and twisted affine cubic Dirac operator. We prove in this setting an analogue of Vogan's conjecture on infinitesimal characters of Harish-Chandra modules in terms of Dirac cohomology. For our calculations we use the machinery of Lie conformal and vertex algebras. 相似文献
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两类幂零的n-Lie代数 总被引:4,自引:1,他引:3
本文提出并构造了两类幂零的n-Lie代数:特征幂零的n-Lie代数与最大秩的幂零的n-Lie代数.证明了n-Lie代数是特征幂零的n-Lie代数的充分必要条件,以及最大秩的幂零的n-Lie代数的结构特征. 相似文献
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Ibrahim Assem 《代数通讯》2013,41(12):4711-4721
We prove that indecomposable transjective modules over cluster-tilted algebras are uniquely determined by their dimension vectors. Similarly, we prove that for cluster-concealed algebras, rigid modules lifting to rigid objects in the corresponding cluster category are uniquely determined by their dimension vectors. Finally, we apply our results to a conjecture of Fomin and Zelevinsky on denominators of cluster variables. 相似文献
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We classify Nichols algebras of irreducible Yetter–Drinfeld modules over nonabelian groups satisfying an inequality for the dimension of the homogeneous subspace of degree two. All such Nichols algebras are finite-dimensional, and all known finite-dimensional Nichols algebras of nonabelian group type appear in the result of our classification. We find a new finite-dimensional Nichols algebra over fields of characteristic two. 相似文献
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AbstractWe previously classified three-dimensional zeropotent algebras over an algebraically closed field of any characteristic except for two. The exceptional case of characteristic two is special because some of the previous transformation matrices to verify isomorphism are unavailable. In this paper, we give new transformation matrices peculiar to characteristic two and then achieve classification in the exceptional case. We thus accomplish a classification of three-dimensional zeropotent algebras over an algebraically closed field of any characteristic. 相似文献
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Joan Felipe Herrera-Granada 《代数通讯》2013,41(5):2180-2192
Grunewald and O'Halloran conjectured in 1993 that every complex nilpotent Lie algebra is the degeneration of another, nonisomorphic, Lie algebra. We prove the conjecture for the class of nilpotent Lie algebras admitting a semisimple derivation, and also for 7-dimensional nilpotent Lie algebras. The conjecture remains open for characteristically nilpotent Lie algebras of dimension grater than or equal to 8. 相似文献
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We introduce a family of braided Hopf algebras that (in characteristic zero) generalizes the rank 1 Hopf algebras introduced by Krop and Radford and we study its cleft extensions. 相似文献
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This is a contribution to the classification of finite-dimensional pointed Hopf algebras. We are concerned with the case when the group of group-like elements is Abelian of exponent 2. We attach to such a pointed Hopf algebra a generalized simply-laced Cartan matrix; we conjecture that the Hopf algebra is finite-dimensional if and only if the Cartan matrix is of finite type. We prove the conjecture for the types An and An(1). We obtain the classification of all possible Hopf algebras with Cartan matrix An. We use the lifting method developed by Hans-Jürgen Schneider and the first-named author.
Presented by S. MontgomeryMathematics Subject Classifications (2000) Primary: 17B37; secondary: 16W30.This work was partially supported by CONICET, Agencia Córdoba Ciencia – CONICOR, FOMEC and Secyt (UNC). 相似文献
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We prove a conjecture of Miemietz and Kashiwara on canonical bases and branching rules of affine Hecke algebras of type D. The proof is similar to the proof of the type B case in Varagnolo and Vasserot (in press) [15]. 相似文献
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Masayoshi Yoshikawa 《代数通讯》2013,41(5):2046-2060
We will investigate the structure of noncommutative imprimitive association schemes of rank 6 and the representation of their adjacency algebras. From this investigation, we will construct new integral standard generalized table algebras with three parameters. These algebras are noncommutative, imprimitive, and 6-dimensional. 相似文献
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The Multiplicity Conjecture is a deep problem relating the multiplicity (or degree) of a Cohen–Macaulay standard graded algebra with certain extremal graded Betti numbers in its minimal free resolution. In the case of level algebras of codimension three, Zanello has proposed a stronger conjecture. We prove this conjecture in the Gorenstein case. 相似文献
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We construct an analogue of von Neumann's affiliated algebras for sofic group algebras over arbitrary fields. Consequently, we settle Kaplansky's direct finiteness conjecture for sofic groups. 相似文献
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Block introduced certain analogues of the Zassenhaus algebras over a field of characteristic 0. The nongraded infinite-dimensional simple Lie algebras of Block type constructed by Xu can be viewed as generalizations of the Block algebras. In this paper, we construct a family of irreducible modules in terms of multiplication and differentiation operators on "polynomials" for four-devivation nongraded Lie algebras of Block type based on the finite-dimensional irreducible weight modules with multiplicity one of general linear Lie algebras. We also find a new series of submodules from which some irreducible quotient modules are obtained. 相似文献
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The connected stable rank and the general stable rank are homotopy invariants for Banach algebras, whereas the Bass stable rank and the topological stable rank should be thought of as dimensional invariants. This paper studies the two homotopical stable ranks, viz. their general properties as well as specific examples and computations. The picture that emerges is that of a strong affinity between the homotopical stable ranks, and a marked contrast with the dimensional ones. 相似文献
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Pairing and Quantum Double of Multiplier Hopf Algebras 总被引:2,自引:0,他引:2
We define and investigate pairings of multiplier Hopf (*-)algebras which are nonunital generalizations of Hopf algebras. Dual pairs of multiplier Hopf algebras arise naturally from any multiplier Hopf algebra A with integral and its dual Â. Pairings of multiplier Hopf algebras play a basic rôle, e.g., in the study of actions and coactions, and, in particular, in the relation between them. This aspect of the theory is treated elsewhere. In this paper we consider the quantum double construction out of a dual pair of multiplier Hopf algebras. We show that two dually paired regular multiplier Hopf (*-)algebras A and B yield a quantum double which is again a regular multiplier Hopf (*-)algebra. If A and B have integrals, then the quantum double also has an integral. If A and B are Hopf algebras, then the quantum double multiplier Hopf algebra is the usual quantum double. The quantum double construction for dually paired multiplier Hopf (*-)algebras yields new nontrivial examples of multiplier Hopf (*-)algebras. 相似文献
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Regina Aragn 《Mathematical Logic Quarterly》1995,41(4):485-504
We consider the theory Thprin of Boolean algebras with a principal ideal, the theory Thmax of Boolean algebras with a maximal ideal, the theory Thac of atomic Boolean algebras with an ideal where the supremum of the ideal exists, and the theory Thsa of atomless Boolean algebras with an ideal where the supremum of the ideal exists. First, we find elementary invariants for Thprin and Thsa. If T is a theory in a first order language and α is a linear order with least element, then we let Sentalg(T) be the Lindenbaum-Tarski algebra with respect to T, and we let intalg(α) be the interval algebra of α. Using rank diagrams, we show that Sentalg(Thprin) ? intalg(ω4), Sentalg(Thmax) ? intalg(ω3) ? Sentalg(Thac), and Sentalg(Thsa) ? intalg(ω2 + ω2). For Thmax and Thac we use Ershov's elementary invariants of these theories. We also show that the algebra of formulas of the theory Tx of Boolean algebras with finitely many ideals is atomic. 相似文献