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1.
We give an equivalence of triangulated categories between the derived category of finitely generated representations of symplectic reflection algebras associated with wreath products (with parameter t=0) and the derived category of coherent sheaves on a crepant resolution of the spectrum of the centre of these algebras.Mathematics Subject Classification (2000): 14E15, 16Rxx, 16S38, 18E30The first author was partially supported by the Nuffield Foundation grant NAL/00625/G and by the University of Washingtons Milliman Fund. The second author was partially supported by an NSF grant DMS-0070560. Both authors are grateful to the Edinburgh Mathematical Society and the Leverhulme Trust for support.Dedicated to Claus Michael Ringel on the occasion of his sixtieth birthday 相似文献
2.
Abstract. – We construct a finitely presented non-amenable group without free non-cyclic subgroups thus providing a finitely
presented counterexample to von Neumann’s problem. Our group is an extension of a group of finite exponent n ≫ 1 by a cyclic group, so it satisfies the identity [x,y]
n
= 1.
Manuscrit reĉu le 8 février 2001.
RID="*"
ID="*"Both authors were supported in part by the NSF grant DMS 0072307. In addition, the research of the first author was
supported in part by the Russian Fund for Basic Research 99-01-00894 and by the INTAS grant, the research of the second author
was supported in part by the NSF grant DMS 9978802. 相似文献
3.
Let U
λ be the union of two unit intervals with gap λ. We show that U
λ is a self-similar set satisfying the open set condition if and only if U
λ can tile an interval by finitely many of its affine copies (admitting different dilations). Furthermore, each such λ can
be characterized as the spectrum of an irreducible double word which represents a tiling pattern. Some further considerations
of the set of all such λ’s, as well as the corresponding tiling patterns, are given.
The first author was partially supported by the RGC grant and the direct grant in CUHK, Fok Ying Tong Education Foundation
and NSFC (10571100). The second author was partially supported by NSFC (70371074) and NFSC (10571104). 相似文献
4.
Birge Zimmermann Huisgen 《manuscripta mathematica》1994,82(1):15-29
It is shown that the little finitistic dimension of a finite dimensional algebra, i.e., the supremum of the finite projective
dimensions attained on finitely generated modules, is not necessarily attained on a cyclic module. In general, arbitrarily
high numbers of generators are required. Moreover, it is demonstrated that this phenomenon may depend on the base fieldk. In fact, for each integerd>-3, there exists a quiver Γ with a set ρ of paths such that the little finitistic dimension of the finite dimensional algebrakΓ/<ρ> is attained on a cyclic module precisely when |k|≥d. By contrast, the global dimension of finite dimensional monomial relation algebras does not depend on the base field.
This research was partially supported by a grant from the National Science Foundation. 相似文献
5.
In previous work arising from the study of Ramanujan's Lost Notebook, a new Abel type lemma was proved. In this paper, we
discuss extensions of this lemma and use it to prove many q-series identities.
The first author was partially supported by NSF grant DMS–0200047. The second author was partially supported by FCT, Portugal,
through program POCTI.
2000 Mathematics Subject Classification:Primary—33D15; Secondary—05A30 相似文献
6.
The Sz.-Nagy-FoiaŞ functional model for completely non-unitary contractions is extended to completely non-coisometric sequences
of bounded operatorsT = (T1,...,T
d) (d finite or infinite) on a Hilbert space, with bounded characteristic functions. For this class of sequences, it is shown
that the characteristic function θT is a complete unitary invariant.
We obtain, as the main result, necessary and sufficient conditions for a bounded multi-analytic operator on Fock spaces to
coincide with the characteristic function associated with a completely non-coisometric sequence of bounded operators on a
Hilbert space.
Research supported in part by a COBASE grant from the National Research Council.
The first author was partially supported by a grant from Ministerul Educaţiei Şi Cercetarii.
The second author was partially supported by a National Science Foundation grant. 相似文献
7.
We prove a q-analogue of the row and column removal theorems for homomorphisms between Specht modules proved by Fayers and the first author [16]. These results can be considered as complements to James and Donkin’s row and column removal theorems for decomposition numbers of the symmetric and general linear groups. In this paper we consider homomorphisms between the Specht modules of the Hecke algebras of type A and between the Weyl modules of the q-Schur algebra.This research was supported by ARC grant DP0343023. The first author was also supported by a Sesqui Research Fellowship at the University of Sydney. 相似文献
8.
Mrinal Raghupathi 《Integral Equations and Operator Theory》2009,63(1):103-125
We study the Nevanlinna-Pick problem for a class of subalgebras of H
∞. This class includes algebras of analytic functions on embedded disks, the algebras of finite codimension in H
∞ and the algebra of bounded analytic functions on a multiply connected domain. Our approach uses a distance formula that generalizes
Sarason’s [23] work. We also investigate the difference between scalar-valued and matrix-valued interpolation through the
use of C
*-envelopes.
This research was partially supported by the NSF grant DMS 0300128. This research was completed as part of my Ph.D. dissertation
at the University of Houston. 相似文献
9.
Separative cancellation for projective modules over exchange rings 总被引:27,自引:0,他引:27
A separative ring is one whose finitely generated projective modules satisfy the propertyA⊕A⋟A⊕B⋟B⊕B⇒A⋟B. This condition is shown to provide a key to a number of outstanding cancellation problems for finitely generated projective
modules over exchange rings. It is shown that the class of separative exchange rings is very broad, and, notably, closed under
extensions of ideals by factor rings. That is, if an exchange ringR has an idealI withI andR/I both separative, thenR is separative.
The research of the first and fourth authors was partially supported by a grant from the DGICYT (Spain) and by the Comissionat
per Universitats i Recerca de la Generalitat de Catalunya. That of the second author was partially supported by a grant from
the NSF (USA). The final version of this paper was prepared while he was visiting the Centre de Recerca Matemàtica, Institut
d'Estudis Catalans in Barcelona, and he thanks the CRM for its hospitality. 相似文献
10.
We prove that Vaught’s conjecture is true for modules over a commutative Prüfer ring. It is shown that a positive solution
to Vaught’s conjecture for modules over 1-dimensional Noetherian domains would imply the same for modules over finitely presented
algebras.
This article was written during the visit of the second author to the University of Manchester supported by EPSRC grant GR/L68827.
She would like to thank the University for hospitality.
Translated fromAlgebra i Logika, Vol. 38, No. 4, pp. 419–435, July–August, 1999. 相似文献
11.
Kenji Nishida 《Algebras and Representation Theory》2006,9(1):13-31
We generalize results of Foxby concerning a commutative Nötherian ring to a certain noncommutative Nötherian algebra Λ over a commutative Gorenstein complete local ring. We assume that Λ is a Cohen–Macaulay isolated singularity having a dualizing module. Then the same method as in the commutative cases works and we obtain a category equivalence between two subcategories of mod Λ, one of which includes all finitely generated modules of finite Gorenstein dimension. We give examples of such algebras which are not Gorenstien; orders related to almost Bass orders and some k-Gorenstein algebras for an integer k.Presented by I. Reiten
★The author is supported by Grant-in-Aid for Scientific Researches B(1) No. 14340007 in Japan. 相似文献
12.
We construct group codes over two letters (i.e., bases of subgroups of a two-generated free group) with special properties.
Such group codes can be used for reducing algorithmic problems over large alphabets to algorithmic problems over a two-letter
alphabet. Our group codes preserve aperiodicity of inverse finite automata. As an application we show that the following problems
are PSpace-complete for two-letter alphabets (this was previously known for large enough finite alphabets): The intersection-emptiness problem for inverse finite
automata, the aperiodicity problem for inverse finite automata, and the closure-under-radical problem for finitely generated
subgroups of a free group. The membership problem for 3-generated inverse monoids is PSpace-complete.
Both authors were supported in part by NSF grant DMS-9970471. The first author was also supported in part by NSF grant CCR-0310793.
The second author acknowledges the support of the Excellency Center, “Group Theoretic Methods for the Study of Algebraic Varieties”
of the Israeli Science Foundation. 相似文献
13.
We show that a compact Riemannian manifold with weakly pointwise 1/4-pinched sectional curvatures is either locally symmetric
or diffeomorphic to a space form. More generally, we classify all compact, locally irreducible Riemannian manifolds M with the property that M × R
2 has non-negative isotropic curvature.
The first author was partially supported by a Sloan Foundation Fellowship and by NSF grant DMS-0605223. The second author
was partially supported by NSF grant DMS-0604960. 相似文献
14.
Jean-Marie Bois 《Mathematische Zeitschrift》2009,262(4):715-741
In this paper we study the minimal number of generators for simple Lie algebras in characteristic 0 or p > 3. We show that any such algebra can be generated by 2 elements. We also examine the ‘one and a half generation’ property,
i.e. when every non-zero element can be completed to a generating pair. We show that classical simple algebras have this property,
and that the only simple Cartan type algebras of type W which have this property are the Zassenhaus algebras.
The author was partially supported by the European Community’s Human Potential Programme under contract HPRN-CT-2002-00287
(RTN Network “K-Theory, Algebraic Groups and Related Structures”) and a long-term research grant from the D.A.A.D. 相似文献
15.
David M. Riley 《Israel Journal of Mathematics》2001,123(1):365-379
The Golod-Shafarevich examples show that not every finitely generated nil algebraA is nilpotent. On the other hand, Kaplansky proved that every finitely generated nil PI-algebra is indeed nilpotent. We generalise
Kaplansky’s result to include those algebras that are only infinitesimally PI. An associative algebraA is infinitesimally PI whenever the Lie subalgebra generated by the first homogeneous component of its graded algebra gr(A)=⊕
t⩾1
A
i
/A
i+1 is a PI-algebra. We apply our results to a problem of Kaplansky’s concerning modular group algebras with radical augmentation
ideal.
The author is supported by NSERC of Canada. 相似文献
16.
A finite, nontrivial algebra is order-primal if its term functions are precisely the monotone functions for some order on the underlying set. We show that the prevariety generated by an order-primal algebra P is relatively congruence-distributive and that the variety generated by P is congruence-distributive if and only if it contains at most two non-ismorphic subdirectly irreducible algebras. We also prove that if the prevarieties generated by order-primal algebras P and Q are equivalent as categories, then the corresponding orders or their duals generate the same order variety. A large class of order-primal algebras is described each member of which generates a variety equivalent as a category to the variety determined by the six-element, bounded ordered set which is not a lattice. These results are proved by considering topological dualities with particular emphasis on the case where there is a monotone near-unanimity function.This research was carried out while the third author held a research fellowship at La Trobe University supported by ARGS grant B85154851. The second author was supported by a grant from the NSERC. 相似文献
17.
In this paper, we prove that the K?hler–Ricci flow converges to a K?hler–Einstein metric when E
1 energy is small. We also prove that E
1 is bounded from below if and only if the K-energy is bounded from below in the canonical class.
The first named author is partially supported by a NSF grant, while the third author was partially supported by a NSF supplement
grant. 相似文献
18.
We show that, if the subgroup growth of a finitely generated (abstract or profinite) groupG is super-exponential, then every finite group occurs as a quotient of a finite index subgroup ofG. The proof involves techniques from finite permutation groups, and depends on the Classification of Finite Simple Groups.The first author was partially supported by the Hungarian National Foundation for Scientific Research, Grant No. T7441. The second author was partially supported by the Israeli National Science Foundation. 相似文献
19.
We show that two C*-algebraic noncommutative tori are strongly Morita equivalent if and only if they have isomorphic ordered K
0-groups and centers, extending N. C. Phillips’s result in the case that the algebras are simple. This is also generalized
to the twisted group C*-algebras of arbitrary finitely generated abelian groups.
This research was supported by a grant from the Natural Sciences and Engineering Research Council of Canada, held by George
A. Elliott. 相似文献
20.
We show that a compact, connected set which has uniform oscillations at all points and at all scales has dimension strictly
larger than 1. We also show that limit sets of certain Kleinian groups have this property. More generally, we show that ifG is a non-elementary, analytically finite Kleinian group, and its limit set Λ(G) is connected, then Λ(G) is either a circle or has dimension strictly bigger than 1.
The first author is partially supported by NSF Grant DMS 95-00577 and an Alfred P. Sloan research fellowship. The second author
is partially supported by NSF grant DMS-94-23746. 相似文献