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Erhard Aichinger 《Algebra Universalis》2002,47(4):425-434
For each we exhibit a finite algebra R
k such that R
k is k-affine complete, but not (k+1)-affine complete; this means that every k-ary congruence preserving function on R
k lies in , but there is a (k +1)-ary congruence preserving function of R
k that does not lie in .
Received September 27, 2001; accepted in final form February 9, 2002. 相似文献
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Presented by E. Fried. 相似文献
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We prove that the class of selfinjective algebras of strictly canonical type, investigated in Kwiecień and Skowroński (2009) [27], Kwiecień and Skowroński (2009) [28], coincides with the class of selfinjective algebras having triangular Galois coverings with infinite cyclic group and the Auslander–Reiten quiver with quasi-tubes maximally saturated by simple and projective modules, satisfying natural conditions. 相似文献
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《Journal of Pure and Applied Algebra》2022,226(7):106943
We provide a simple and conceptual proof of Du-Fu's multiplication formula of affine q-Schur algebras via Lusztig's formula. We use the multiplication formulas to provide a proof of the existence of generic affine Schur algebras, in return, and a formula of the generators under comultiplication. 相似文献
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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
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Haisheng Li 《Mathematische Zeitschrift》2004,248(3):635-664
In this paper, we exploit basic formal variable techniques to study certain categories of modules for an (untwisted) affine Lie algebra , motivated by Chari-Pressleys work on certain integrable modules. We define and study two categories and of -modules using generating functions, where is proved to contain the well known evaluation modules and to unify highest weight modules, evaluation modules and their tensor product modules. We classify integrable irreducible -modules in categories and and we determine the isomorphism classes of those irreducible modules. Finally we prove a result that relates fusion rules in the context of vertex operator algebras with integrable irreducible modules of Chari-Pressley.in final form: 12 November 2003Partially supported by a NSA grant and a grant from Rutgers Research Council. 相似文献
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A flat complete causal Lorentzian manifold is called strictly causal if the past and future of its every point are closed near this point. We consider the strictly causal manifolds with unipotent holonomy groups and assign to a manifold of this type four nonnegative integers (a signature) and a parabola in the cone of positive definite matrices. Two manifolds are equivalent if and only if their signatures coincide and the corresponding parabolas are equal (up to a suitable automorphism of the cone and an affine change of variable). Also, we give necessary and sufficient conditions distinguishing the parabolas of this type among all parabolas in the cone. 相似文献
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We announce the construction of an explicit basis for all integrable highest weight modules over the Lie algebra A
1
(1). The construction uses representations of vertex operator algebras and leads to combinatorial identities of Rogers-Ramanujan-type. 相似文献
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F. RadÓ 《Results in Mathematics》1979,2(1-2):171-185
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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
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