共查询到20条相似文献,搜索用时 15 毫秒
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A. Caranti 《Israel Journal of Mathematics》1999,109(1):61-73
The simple, modular Lie algebras of Zassenhaus have peculiar features in characteristic three. Their second cohomology groups
are larger than in characteristicp>3, and they possess a non-degenerate associative form. These properties are reflected in the presentations of certain loop
algebras of these algebras, that arise naturally in analogy with the graded Lie algebra associated to the Nottingham group
with respect to its lower central series.
Partially supported by MURST, Italy. The author is a member of CNR-GNSAGA, Italy. The author is grateful to the Mathematisches
Forschungsinstitut Oberwolfach for the kind hospitality while part of this work was being written. 相似文献
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Archiv der Mathematik - We give another proof of the recent result of Ringel, which asserts equality between the finitistic dimension and delooping level of Nakayama algebras. The main tool is the... 相似文献
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S. P. Mishchenko 《Mathematical Notes》1990,47(4):368-372
Translated from Matematicheskie Zametki, Vol. 47, No. 4, pp. 83–89, April, 1990. 相似文献
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The hermitian level of composition algebras with involution over a ring is studied. In particular, it is shown that the hermitian
level of a composition algebra with standard involution over a semilocal ring, where two is invertible, is always a power
of two when finite. Furthermore, any power of two can occur as the hermitian level of a composition algebra with non-standard
involution. Some bounds are obtained for the hermitian level of a composition algebra with involution of the second kind.
Received: 22 March 2002 / Revised version: 10 July 2002
Mathematics Subject Classification (2000): 17A75, 16W10, 11E25 相似文献
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Katrina Barron Nathan Vander Werf Jinwei Yang 《Journal of Pure and Applied Algebra》2019,223(8):3295-3317
Motivated by the study of indecomposable, nonsimple modules for a vertex operator algebra V, we study the relationship between various types of V-modules and modules for the higher level Zhu algebras for V, denoted , for , first introduced by Dong, Li, and Mason in 1998. We resolve some issues that arise in a few theorems previously presented when these algebras were first introduced, and give examples illustrating the need for certain modifications of the statements of those theorems. We establish that whether or not is isomorphic to a direct summand of affects the types of indecomposable V-modules which can be constructed by inducing from an -module, and in particular whether there are V-modules induced from -modules that were not already induced by . We give some characterizations of the V-modules that can be constructed from such inducings, in particular as regards their singular vectors. To illustrate these results, we discuss two examples of : when V is the vertex operator algebra associated to either the Heisenberg algebra or the Virasoro algebra. For these two examples, we show how the structure of in relationship to determines what types of indecomposable V-modules can be induced from a module for the level zero versus level one Zhu algebras. We construct a family of indecomposable modules for the Virasoro vertex operator algebra that are logarithmic modules and are not highest weight modules. 相似文献
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In the present paper we obtain a list of algebras, up to isomorphism, such that the closure of any complex finite-dimensional algebra contains one of the algebras of the given list. 相似文献
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The Hecke group algebra of a finite Coxeter group , as introduced by the first and last authors, is obtained from by gluing appropriately its 0-Hecke algebra and its group algebra. In this paper, we give an equivalent alternative construction in the case when is the finite Weyl group associated to an affine Weyl group W. Namely, we prove that, for q not a root of unity of small order, is the natural quotient of the affine Hecke algebra H(W)(q) through its level 0 representation.The proof relies on the following core combinatorial result: at level 0 the 0-Hecke algebra H(W)(0) acts transitively on . Equivalently, in type A, a word written on a circle can be both sorted and antisorted by elementary bubble sort operators. We further show that the level 0 representation is a calibrated principal series representation M(t) for a suitable choice of character t, so that the quotient factors (non-trivially) through the principal central specialization. This explains in particular the similarities between the representation theory of the 0-Hecke algebra and that of the affine Hecke algebra H(W)(q) at this specialization. 相似文献
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Vyjayanthi Chari 《Advances in Mathematics》2009,220(4):1193-328
Let g be a finite-dimensional simple Lie algebra and let Sg be the locally finite part of the algebra of invariants (EndCV⊗Sg(g)) where V is the direct sum of all simple finite-dimensional modules for g and S(g) is the symmetric algebra of g. Given an integral weight ξ, let Ψ=Ψ(ξ) be the subset of roots which have maximal scalar product with ξ. Given a dominant integral weight λ and ξ such that Ψ is a subset of the positive roots we construct a finite-dimensional subalgebra of Sg and prove that the algebra is Koszul of global dimension at most the cardinality of Ψ. Using this we construct naturally an infinite-dimensional non-commutative Koszul algebra of global dimension equal to the cardinality of Ψ. The results and the methods are motivated by the study of the category of finite-dimensional representations of the affine and quantum affine algebras. 相似文献
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We classify certain non-linear Lie conformal algebras with three generators, which can be viewed as deformations of the current
Lie conformal algebra of sℓ
2. In doing so we discover an interesting 1-parameter family of non-linear Lie conformal algebras and the corresponding freely generated vertex algebras , which includes for d = 1 the affine vertex algebra of sℓ
2 at the critical level k = –2. We construct free-field realizations of the algebras extending the Wakimoto realization of at the critical level, and we compute their Zhu algebras.
Dedicated to our teacher Victor Kac on the occasion of his 65th birthday 相似文献
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We define a higher level version of the affine Hecke algebra and prove that, after completion, this algebra is isomorphic to a completion of Webster's tensor product algebra of type A. We then introduce a higher level version of the affine Schur algebra and establish, again after completion, an isomorphism with the quiver Schur algebra. An important observation is that the higher level affine Schur algebra surjects to the Dipper-James-Mathas cyclotomic q-Schur algebra. Moreover, we give nice diagrammatic presentations for all the algebras introduced in this paper. 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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Junzo Watanabe 《Proceedings of the American Mathematical Society》1998,126(11):3161-3168
Let be a field of characteristic 0. If is a complete intersection generated by three homogeneous elements of degrees with , then the reduction of by a general linear form is minimally generated by three elements if and only if .