共查询到20条相似文献,搜索用时 31 毫秒
1.
Alexander Kuznetsov 《Selecta Mathematica, New Series》2008,13(4):661-696
Let Y be a singular algebraic variety and let
be a resolution of singularities of Y. Assume that the exceptional locus of
over Y is an irreducible divisor
in
. For every Lefschetz decomposition of the bounded derived category
of coherent sheaves on
we construct a triangulated subcategory
) which gives a desingularization of
. If the Lefschetz decomposition is generated by a vector bundle tilting over Y then
is a noncommutative resolution, and if the Lefschetz decomposition is rectangular, then
is a crepant resolution. 相似文献
2.
Muneo Chō Mariko Giga Tadasi Huruya Takeaki Yamazaki 《Integral Equations and Operator Theory》2007,57(3):303-308
Let
be an invertible class A operator such that
. Then we show that
, where gT is the principal function of T. Moreover, we show that if T is pure, then
. 相似文献
3.
Non-group-theoretical semisimple Hopf algebras from group actions on fusion categories 总被引:1,自引:0,他引:1
Dmitri Nikshych 《Selecta Mathematica, New Series》2008,14(1):145-161
Given an action of a finite group G on a fusion category we give a criterion for the category of G-equivariant objects in to be group-theoretical, i.e., to be categorically Morita equivalent to a category of group-graded vector spaces. We use
this criterion to answer affirmatively the question about existence of non-group-theoretical semisimple Hopf algebras asked
by P. Etingof, V. Ostrik, and the author in [7]. Namely, we show that certain /2-equivariantizations of fusion categories constructed by D. Tambara and S. Yamagami [26] are equivalent to representation
categories of non-group-theoretical semisimple Hopf algebras. We describe these Hopf algebras as extensions and show that
they are upper and lower semisolvable.
相似文献
4.
Let
be a compact Riemannian manifold without boundary. In this paper, we consider the first nonzero eigenvalue of the p-Laplacian
and we prove that the limit of
when
is 2/d(M), where d(M) is the diameter of M. Moreover, if
is an oriented compact hypersurface of the Euclidean space
or
, we prove an upper bound of
in terms of the largest principal curvature κ over M. As applications of these results, we obtain optimal lower bounds of d(M) in terms of the curvature. In particular, we prove that if M is a hypersurface of
then:
.
Mathematics Subject Classifications (2000): 53A07, 53C21. 相似文献
5.
Mohamed Bendaoud 《Archiv der Mathematik》2009,92(3):257-265
Let be a complex Hilbert space and let be the algebra of all bounded linear operators on . We characterize additive maps from onto itself preserving different spectral quantities such as the minimum modulus, the surjectivity modulus, and the maximum
modulus of operators.
Received: 15 July 2008 相似文献
6.
A. Polishchuk 《Selecta Mathematica, New Series》2007,13(3):531-569
In this paper we construct and study the actions of certain deformations of the Lie algebra of Hamiltonians on the plane on
the Chow groups (resp., cohomology) of the relative symmetric powers and the relative Jacobian of a family of curves . As one of the applications, we show that in the case of a single curve C this action induces a -form of a Lefschetz sl2- action on the Chow groups of C
[N]. Another application gives a new grading on the ring CH
0(J) of 0-cycles on the Jacobian J of C (with respect to the Pontryagin product) and equips it with an action of the Lie algebra of vector fields on the line. We
also define the groups of tautological classes in CH and in CH and prove for them analogs of the properties established in the case of the Jacobian of a single curve by Beauville in [5].
We show that our algebras of operators preserve the subrings of tautological cycles and act on them as some explicit differential
operators.
This work was partially supported by the NSF grant DMS-0601034. 相似文献
7.
Let M be a right R-module,
the class of all M-small modules, and P a projective cover of M in
[M]. We consider the torsion theories
= (
),
= (
), and
= (
) in
[M], where
is the torsion theory generated by
is the torsion theory cogenerated by
, and
is the dual Lambek torsion theory. We study some conditions for
to be cohereditary, stable, or split, and prove that Rej(M,
) = M
=
(=
=
)
=
GenM(P)
.2000 Mathematics Subject Classification: 16S90 相似文献
8.
Let m ≥ 1 be an integer and N > 2m. Let μ be a positive Radon measure on . We study necessary and sufficient conditions on possible distributional solutions of , that guarantee the validity of the representation formula a.e. on , where and c(2m) is a positive constant depending on m and N. Several consequences are derived. In particular we prove Liouville theorems for systems of higher order elliptic inequalities
and weighted form of Hardy-Littlewood-Sobolev systems of integral equations.
Received: March 2008 相似文献
9.
We consider quantum Schubert cells in the quantum grassmannian and give a cell decomposition of the prime spectrum via the
Schubert cells. As a consequence, we show that all primes are completely prime in the generic case where the deformation parameter
q is not a root of unity. There is a natural torus action of
on the quantum grassmannian
and the cell decomposition of the set of
-primes leads to a parameterisation of the
-spectrum via certain diagrams on partitions associated to the Schubert cells. Interestingly, the same parameterisation occurs
for the nonnegative cells in recent studies concerning the totally nonnegative grassmannian. Finally, we use the cell decomposition
to establish that the quantum grassmannian satisfies normal separation and catenarity. 相似文献
10.
D. Jakubíková-Studenovská 《Algebra Universalis》2009,60(2):125-143
In the present paper we prove that the collection of all convexities of partial monounary algebras is finite; namely, it has exactly 23 elements. Further, we show that for
each element there exists a subset of such that is generated by and card .
This work was supported by the Science and Technology Assistance Agency under the contract No. APVT-20-004104. Supported by
Grant VEGA 1/3003/06. 相似文献
11.
Humio Ichimura 《Archiv der Mathematik》2006,87(6):539-545
Let p be an odd prime number and
. Let
be the classical Stickelberger ideal of the group ring
. Iwasawa [6] proved that the index
equals the relative class number
of
. In [2], [4] we defined for each subgroup H of G a Stickelberger ideal
of
, and studied some of its properties. In this note, we prove that when
mod 4 and [G : H] = 2, the index
equals the quotient
.
Received: 13 January 2006 相似文献
12.
The peak algebra
is a unital subalgebra of the symmetric group algebra, linearly spanned by sums of permutations with a common set of peaks.
By exploiting the combinatorics of sparse subsets of [n−1] (and of certain classes of compositions of n called almost-odd and thin), we construct three new linear bases of
. We discuss two peak analogs of the first Eulerian idempotent and construct a basis of semi-idempotent elements for the peak
algebra. We use these bases to describe the Jacobson radical of
and to characterize the elements of
in terms of the canonical action of the symmetric groups on the tensor algebra of a vector space. We define a chain of ideals
of
, j = 0,...,
, such that
is the linear span of sums of permutations with a common set of interior peaks and
is the peak algebra. We extend the above results to
, generalizing results of Schocker (the case j = 0).
Aguiar supported in part by NSF grant DMS-0302423
Orellana supported in part by the Wilson Foundation 相似文献
13.
Let G be a split adjoint semisimple group over
and
a maximal compact subgroup. We shall give a uniform, short and essentially elementary proof of the Weyl law for cusp forms
on congruence quotients of
. This proves a conjecture of Sarnak for
-split groups, previously known only for the case G = PGL(n). The key idea amounts to a new type of simple trace formula.
Received: April 2005 Revision: June 2006 Accepted: October 2006 相似文献
14.
We prove that for any continuous piecewise monotone or smooth interval map f and any subset
of the set of periods of periodic trajectories of f, there is another map
such that the set of periods of periodic trajectories common for f and
, which is denoted by
, coincides with
. At the same time, for each integer
, there exists a continuous map f such that
for any map
if
is an infinite set.
Dedicated to Vladimir Igorevich Arnold 相似文献
15.
We consider the semilinear reaction diffusion equation
, in a bounded domain . We assume the standard “Allen-Cahn-type” nonlinearity, while V is either the inverse square potential or the borderline potential (thus including the classical Allen-Cahn-type equation as a special case when ). In the subcritical cases and where is the optimal constant of Hardy and Hardy-type inequalities), we present a new estimate on the dimension of the global attractor.
This estimate comes out by an improved lower bound for sums of eigenvalues of the Laplacian by A. D. Melas (Proc. Amer. Math.
Soc. 131 (2003), 631–636). The estimate is sharp, revealing the existence of (an explicitly given) threshold value for the ratio of
the volume to the moment of inertia of Ω on which the dimension of the attractor may considerably change. Consideration is
also given on the finite dimensionality of the global attractor in the critical case
Received: 7 May 2008 相似文献
16.
Vasily A. Prokhorov Edward B. Saff Maxim Yattselev 《Complex Analysis and Operator Theory》2009,3(2):501-524
Let be a bounded simply connected domain with boundary Γ and let be a regular compact set with connected complement. In this paper we investigate asymptotics of the extremal constants:
where is the supremum norm on a compact set K, is the set of all algebraic polynomials of degree at most m, and as . Subsequently, we obtain asymptotic behavior of the Kolmogorov k-widths, , of the unit ball An∞ of restricted to E in C(E), where H∞ is the Hardy space of bounded analytic functions on G and C(E) is the space of continuous functions on E.
Received: April 24, 2008. Accepted: May 15, 2008. 相似文献
17.
Amol Sasane 《Complex Analysis and Operator Theory》2009,3(1):323-330
Let E be a separable infinite-dimensional Hilbert space, and let denote the algebra of all functions that are holomorphic. If is a subalgebra of , then using an algebraic result of Corach and Larotonda, we derive that under some conditions, the Bass stable rank of is infinite. In particular, we deduce that the Bass (and hence topological stable ranks) of the Hardy algebra , the disk algebra and the Wiener algebra are all infinite.
Submitted: October 10, 2007., Revised: January 11, 2008., Accepted: January 12, 2007. 相似文献
18.
Yury M. Arlinskiĭ Seppo Hassi Henk S. V. de Snoo 《Complex Analysis and Operator Theory》2009,3(1):19-56
Passive systems with and as an input and output space and as a state space are considered in the case that the main operator on the state space is normal. Basic properties are given
and a general unitary similarity result involving some spectral theoretic conditions on the main operator is established.
A passive system with is said to be quasi-selfadjoint if ran . The subclass of the Schur class is the class formed by all transfer functions of quasi-selfadjoint passive systems. The subclass is characterized and minimal passive quasi-selfadjoint realizations are studied. The connection between the transfer function
belonging to the subclass and the Q-function of T is given.
Received: December 16, 2007., Accepted: March 4, 2008. 相似文献
19.
Yury M. Arlinskiĭ Seppo Hassi Henk S. V. de Snoo 《Complex Analysis and Operator Theory》2007,1(2):211-233
Passive linear systems τ =
have their transfer function
in the Schur class S
. Using a parametrization of contractive block operators the transfer function
is connected to the Sz.-Nagy–Foiaş characteristic function
of the contraction A. This gives a new aspect and some explicit formulas for studying the interplay between the system τ and the functions
and
. The method leads to some new results for linear passive discrete-time systems. Also new proofs for some known facts in
the theory of these systems are obtained.
Dedicated to Eduard Tsekanovskiĭ on the occasion of his seventieth birthday
This work was supported by the Research Institute for Technology at the University of Vaasa.
The first author was also supported by the Academy of Finland (projects 212146, 117617) and the Dutch Organization for Scientific
Research N.W.O. (B 61-553).
Received: December 22, 2006. Revised: February 6, 2007. 相似文献
20.
Gregory D. Landweber 《K-Theory》2005,36(1-2):115-168
Given a Lie superalgebra
, we introduce several variants of the representation ring, built as subrings and quotients of the ring
of virtual
-supermodules, up to (even) isomorphisms. In particular, we consider the ideal
of virtual
-supermodules isomorphic to their own parity reversals, as well as an equivariant K-theoretic super representation ring
on which the parity reversal operator takes the class of a virtual
-supermodule to its negative. We also construct representation groups built from ungraded
-modules, as well as degree-shifted representation groups using Clifford modules. The full super representation ring
, including all degree shifts, is then a
-graded ring in the complex case and a
-graded ring in the real case. Our primary result is a six-term periodic exact sequence relating the rings
, and
. We first establish a version of it working over an arbitrary (not necessarily algebraically closed) field of characteristic
0. In the complex case, this six-term periodic long exact sequence splits into two three-term sequences, which gives us additional
insight into the structure of the complex super representation ring
. In the real case, we obtain the expected 24-term version, as well as a surprising six-term version, of this periodic exact
sequence.
(Received: October 2004) 相似文献