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1.
A classifications is presented of the parabolic decompositions of the system of roots of Kac- Moody algebras of rank 2. New series of irreducible representations are constructed.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 12, pp. 1712–1715, December, 1992. 相似文献
2.
In this paper,based on Kac-Moody algebra,the isomorphic realization of nondegenerate solvable Lie algebras of maximal rank is given,which in turn revels the closed connections between nondegenerate solvable Lie algebras and Kac-Moody algebras,resulting in some new worthy topics in this area. 相似文献
3.
Tubular algebras and affine Kac-Moody algebras 总被引:1,自引:0,他引:1
Zheng-xin CHEN & Ya-nan LIN School of Mathematics Computer Science Pujian Normal University Fuzhou China School of Mathematical Sciences Xiamen University Xiamen China 《中国科学A辑(英文版)》2007,50(4):521-532
The purpose of this paper is to construct quotient algebras L(A)1C/I(A) of complex degenerate composition Lie algebras L(A)1C by some ideals, where L(A)1C is defined via Hall algebras of tubular algebras A, and to prove that the quotient algebras L(A)1C/I(A) are isomorphic to the corresponding affine Kac-Moody algebras. Moreover, it is shown that the Lie algebra Lre(A)1C generated by A-modules with a real root coincides with the degenerate composition Lie algebra L(A)1C generated by simple A-modules. 相似文献
4.
M. V. Zaitsev 《Mathematical Notes》1997,62(1):80-86
In this paper the identities of the complex affine Kac-Moody algebras are studied. It is proved that the identities of twisted
affine algebras coincide with those of the corresponding nontwisted algebras. Moreover, in the class of nontwisted affine
Kac-Moody algebras, each of these algebras is uniquely defined by its identities. It is shown that the varieties of affine
algebras, as well as the varieties defined by finitely generated three-step solvable Lie algebras, have exponential growth.
Translated fromMatematicheskie Zametki, Vol. 62 No. 1, pp. 95–102, July 1997.
Translated by A. I. Shtern 相似文献
5.
Given any Coxeter group, we define rigid reflections and rigid roots using non-self-intersecting curves on a Riemann surface with labeled curves. When the Coxeter group arises from an acyclic quiver, they are related to the rigid representations of the quiver. For a family of rank 3 Coxeter groups, we show that there is a surjective map from the set of reduced positive roots of a rank 2 Kac-Moody algebra onto the set of rigid reflections. We conjecture that this map is bijective. 相似文献
6.
Triangulated categories and Kac-Moody algebras 总被引:7,自引:0,他引:7
By using the Ringel-Hall algebra approach, we find a Lie algebra arising in each triangulated category with T 2=1, where T is the translation functor. In particular, the generic form of the Lie algebras determined by the root categories, the 2-period orbit categories of the derived categories of finite dimensional hereditary associative algebras, gives a realization of all symmetrizable Kac-Moody Lie algebras. Oblatum 4-XII-1998 & 11-XI-1999?Published online: 21 February 2000 相似文献
7.
We determine the maximal graded subalgebras of affine Kac-Moody algebras. We also show that the maximal graded subalgebras
of loop algebras are essentially loop algebras.
Supported by the Binational Science Foundation United States — Israel, Grant No. 92-00034. 相似文献
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9.
Thomas Foertsch Viktor Schroeder 《Proceedings of the American Mathematical Society》2005,133(2):557-563
Generalizing a result of Brady and Farb (1998), we prove the existence of a bilipschitz embedded manifold of negative curvature bounded away from zero and dimension in the product of two Hadamard manifolds of dimension with negative curvature bounded away from zero.
Combining this result with a result of Buyalo and Schroeder (2002), we prove the additivity of the hyperbolic rank for products of manifolds with negative curvature bounded away from zero.
10.
Michael Kleber 《Advances in Mathematics》2006,201(1):1-35
We consider a large class of series of symmetrizable Kac-Moody algebras (generically denoted Xn). This includes the classical series An as well as others like En whose members are of Indefinite type. The focus is to analyze the behavior of representations in the limit n→∞. Motivated by the classical theory of An=sln+1C, we consider tensor product decompositions of irreducible highest weight representations of Xn and study how these vary with n. The notion of “double-headed” dominant weights is introduced. For such weights, we show that tensor product decompositions in Xn do stabilize, generalizing the classical results for An. The main tool used is Littelmann's celebrated path model. One can also use the stable multiplicities as structure constants to define a multiplication operation on a suitable space. We define this so-called stable representation ring and show that the multiplication operation is associative. 相似文献
11.
Kenneth R. Davidson Stephen C. Power Dilian Yang 《Journal of Functional Analysis》2008,255(4):819-853
We provide a detailed analysis of atomic ∗-representations of rank 2 graphs on a single vertex. They are completely classified up to unitary equivalence, and decomposed into a direct sum or direct integral of irreducible atomic representations. The building blocks are described as the minimal ∗-dilations of defect free representations modelled on finite groups of rank 2. 相似文献
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13.
Representations of groups of loops in U(N), SO(N) and various subgroups are studied. The representations are defined on fermion Fock spaces, and may be regarded as local gauge groups in the context of the two-dimensional many-particle Dirac theory for charged or neutral particles with rest mass m0. For m=0, the representations are shown to give rise to type I factors, while for m>0 hyperfinite, type III1 factors arise. A key point in the structure analysis is a convergence result: We prove that suitably rescaled representers of certain nonzero winding number loops converge to the free Dirac fields. We also present applications to cyclicity and irreducibility questions concerning the Dirac currents, and to the representation theory of a class of Kac-Moody Lie algebras. 相似文献
14.
A lot of recent activity in the theory of cluster algebras has been directed toward various constructions of “natural” bases in them. One of the approaches to this problem was developed several years ago by Sherman and Zelevinsky who have shown that the indecomposable positive elements form an integer basis in any rank 2 cluster algebra of finite or affine type. It is strongly suspected (but not proved) that this property does not extend beyond affine types. Here, we go around this difficulty by constructing a new basis in any rank 2 cluster algebra that we call the greedy basis. It consists of a special family of indecomposable positive elements that we call greedy elements. Inspired by a recent work of Lee and Schiffler; Rupel, we give explicit combinatorial expressions for greedy elements using the language of Dyck paths. 相似文献
15.
Cristian Lenart Alexander Postnikov 《Transactions of the American Mathematical Society》2008,360(8):4349-4381
We present a simple combinatorial model for the characters of the irreducible integrable highest weight modules for complex symmetrizable Kac-Moody algebras. This model can be viewed as a discrete counterpart to the Littelmann path model. We describe crystal graphs and give a Littlewood-Richardson rule for decomposing tensor products of irreducible representations. The new model is based on the notion of a -chain, which is a chain of positive roots defined by certain interlacing conditions.
16.
Based on the n-fold tensor product version of the generalized double-bosonization construction, we prove the Majid conjecture of the quantum Kac-Moody algebras version. Particularly, we give explicitly the double-bosonization type-crossing constructions of quantum Kac-Moody algebras for affine types , ,and Tp,q,r, and in this way, we can recover generators of quantum Kac-Moody algebras with braided groups defined by R-matrices in the related braided tensor category. This gives us a better understanding for the algebra structures themselves of the quantum Kac-Moody algebras as a certain extension of module-algebras/module-coalgebras with respect to the related quantum subalgebras of finite types inside. 相似文献
17.
A conjecture of Kac states that the polynomial counting the number of absolutely indecomposable representations of a quiver over a finite field with given dimension vector has positive coefficients and furthermore that its constant term is equal to the multiplicity of the corresponding root in the associated Kac-Moody Lie algebra. In this paper we prove these conjectures for indivisible dimension vectors. Dedicated to Idun Reiten on the occasion of her sixtieth birthdayMathematics Subject Classification (1991) 16G20, 17B67 相似文献
18.
Seok-Jin Kang 《Mathematische Annalen》1994,298(1):373-384
Research at MSRI supported in part by NSF Grant #DMS 9022140 相似文献
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We show that every Kac-Moody Lie algebra of indefinite type contains a subalgebra with a Dynkin diagram having two adjacent vertices whose edge labels multiply to a number greater than or equal to five. Consequently, every Kac-Moody algebra of indefinite type contains a subalgebra of strictly hyperbolic type, and a free Lie algebra of rank two. 相似文献