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1.
Pu Zhang 《Journal of Algebra》2002,250(2):709
Generalized Green classes are introduced; some basic properties of members in a generalized Green class are studied. Finally, we apply the results to
(Λ), the Ringel–Hall algebra of a finite-dimensional hereditary algebra Λ over a finite field. In particular, it is proved that
(Λ) belongs to a suitable generalized Green class, and that there is direct decomposition of spaces
(Λ) =
(Λ) J, where
(Λ) is the composition algebra of Λ and J is a twisted Hopf ideal of
(Λ), which is exactly the orthogonal complement of
(Λ). 相似文献
2.
Let
be an algebraic algebra over an infinite field K and let
(
) be its group of units. We prove a stronger version of Hartley's conjecture for
, namely, if a Laurent polynomial identity (LPI, for short) f = 0 is satisfied in
(
), then
satisfies a polynomial identity (PI). We also show that if
is non-commutative, then
is a PI-ring, provided f = 0 is satisfied by the non-central units of
. In particular,
is locally finite and, thus, the Kurosh problem has a positive answer for K-algebras whose unit group is LPI. Moreover, f = 0 holds in
(
) if and only if the same identity is satisfied in
. The last fact remains true for generalized Laurent polynomial identities, provided that
is locally finite. 相似文献
3.
Julien Bichon 《Journal of Algebra》2000,230(2):83
Let
be a (small) category and let F:
→
algf be a functor, where
algf is the category of finite-dimensional measured algebras over a field k (or Frobenius algebras). We construct a universal Hopf algebra Aaut(F) such that F factorizes through a functor
:
→
coalgf(Aaut(F)), where
coalgf(Aaut(F)) is the category of finite-dimensional measured Aaut(F)-comodule algebras. This general reconstruction result allows us to recapture a finite-dimensional Hopf algebra A from the category
coalgf(A) and the forgetful functor ω:
coalgf(A) →
algf: we have A Aaut(ω). Our universal construction is also done in a C*-algebra framework, and we get compact quantum groups in the sense of Woronowicz. 相似文献
4.
Let I be a finite interval, , and 1p∞. Given a set M, of functions defined on I, denote by the subset of all functions yM such that the s-difference is nonnegative on I, τ>0. Further, denote by the Sobolev class of functions x on I with the seminorm x(r)Lp1. We obtain the exact orders of the Kolmogorov and the linear widths, and of the shape-preserving widths of the classes in Lq for s>r+1 and (r,p,q)≠(1,1,∞). We show that while the widths of the classes depend in an essential way on the parameter s, which characterizes the shape of functions, the shape-preserving widths of these classes remain asymptotically ≈n-2. 相似文献
5.
We study the Kolmogorov n-widths and the linear n-widths of weighted Sobolev classes on the unit ball Bd in Lq,μ, where Lq,μ, 1≤q≤∞, denotes the weighted Lq space of functions on Bd with respect to weight . Optimal asymptotic orders of and as n→∞ are obtained for all 1≤p,q≤∞ and μ≥0. 相似文献
6.
Maxim Nazarov 《European Journal of Combinatorics》2004,25(8):1345-1376
Let
be the affine Hecke algebra corresponding to the group GLl over a p-adic field with residue field of cardinality q. We will regard
as an associative algebra over the field
. Consider the
-module W induced from the tensor product of the evaluation modules over the algebras
and
. The module W depends on two partitions λ of l and μ of m, and on two non-zero elements of the field
. There is a canonical operator J acting on W; it corresponds to the trigonometric R-matrix. The algebra
contains the finite dimensional Hecke algebra Hl+m as a subalgebra, and the operator J commutes with the action of this subalgebra on W. Under this action, W decomposes into irreducible subspaces according to the Littlewood–Richardson rule. We compute the eigenvalues of J, corresponding to certain multiplicity-free irreducible components of W. In particular, we give a formula for the ratio of two eigenvalues of J, corresponding to the “highest” and the “lowest” components. As an application, we derive the well known q-analogue of the hook-length formula for the number of standard tableaux of shape λ. 相似文献
7.
Richard F. Bass Krzysztof Burdzy 《Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques》2001,37(6):627
For
, we consider Lft, the local time of space-time Brownian motion on the curve f. Let
be the class of all functions whose Hölder norm of order α is less than or equal to 1. We show that the supremum of Lf1 over f in
is finite if α>1/2 and infinite if α<1/2. 相似文献
8.
Given a subset E of convex functions from
into
which satisfy growth conditions of order p>1 and an open bounded subset
of
, we establish the continuity of a map μΦμ from the set of all Young measures on
equipped with the narrow topology into a set of suitable functionals defined in
and equipped with the topology of Γ-convergence. Some applications are given in the setting of periodic and stochastic homogenization. 相似文献
9.
Let X be a smooth toric variety. Cox introduced the homogeneous coordinate ring S of X and its irrelevant ideal
. Let A denote the ring of differential operators on Spec(S). We show that the category of
-modules on X is equivalent to a subcategory of graded A-modules modulo
-torsion. Additionally, we prove that the characteristic variety of a
-module is a geometric quotient of an open subset of the characteristic variety of the associated A-module and that holonomic
-modules correspond to holonomic A-modules. 相似文献
10.
S. V. Khrushchev 《Journal of Approximation Theory》2002,116(2):268-342
The set
of all probability measures σ on the unit circle
splits into three disjoint subsets depending on properties of the derived set of {|n|2dσ}n0, denoted by Lim(σ). Here {n}n0 are orthogonal polynomials in L2(dσ). The first subset is the set of Rakhmanov measures, i.e., of σ
with {m}=Lim(σ), m being the normalized (m(
)=1) Lebesgue measure on
. The second subset Mar(
) consists of Markoff measures, i.e., of σ
with mLim(σ), and is in fact the subject of study for the present paper. A measure σ, belongs to Mar(
) iff there are >0 and l>0 such that sup{|an+j|:0jl}>, n=0,1,2,…,{an} is the Geronimus parameters (=reflectioncoefficients) of σ. We use this equivalence to describe the asymptotic behavior of the zeros of the corresponding orthogonal polynomials (see Theorem G). The third subset consists of σ
with {m}Lim(σ). We show that σ is ratio asymptotic iff either σ is a Rakhmanov measure or σ satisfies the López condition (which implies σMar(
)). Measures σ satisfying Lim(σ)={ν} (i.e., weakly asymptotic measures) are also classified. Either ν is the sum of equal point masses placed at the roots of zn=λ, λ
, n=1,2,…, or ν is the equilibrium measure (with respect to the logarithmic kernel) for the inverse image under an m-preserving endomorphism z→zn, n=1,2,…, of a closed arc J (including J=
) with removed open concentric arc J0 (including J0=). Next, weakly asymptotic measures are completely described in terms of their Geronimus parameters. Finally, we obtain explicit formulae for the parameters of the equilibrium measures ν and show that these measures satisfy {ν}=Lim(ν). 相似文献
11.
The following reaction-diffusion system in spatially non-homogeneous almost-periodic media is considered in a bounded domain
: (1) ∂tu=Au−f(u)+g, u|∂Ω=0. Here u=(u1,…,uk) is an unknown vector-valued function, f is a given nonlinear interaction function and the second order elliptic operator A has the following structure: where aijl(y) are given almost-periodic functions. We prove that, under natural assumptions on the nonlinear term f(u), the longtime behavior of solutions of (1) can be described in terms of the global attractor
of the associated dynamical system and that the attractors
, 0<<01, converge to the attractor
of the homogenized problem (1) as →0. Moreover, in the particular case of periodic media, we give explicit estimates for the distance between the non-homogenized
and the homogenized
attractors in terms of the parameter . 相似文献
12.
Let C
n and C
n be the varieties of all completely regular and of all completely simple semigroups, respectively, whose idempotent generated subsemigroups are periodic with period n. We use Ol'shanski
's theory of geometric group presentations to show that for large odd n these varieties (and similarly defined varieties of epigroups) do not have finitely axiomatizable equational theories. 相似文献
13.
We present sharp bounds on the Kolmogorov probabilistic (N,δ)-width and p-average N-width of multivariate Sobolev space with mixed derivative
, equipped with a Gaussian measure μ in
, that is where 1<q<∞,0<p<∞, and ρ>1 is depending only on the eigenvalues of the correlation operator of the measure μ (see (4)). 相似文献
Full-size image (1K)
14.
In 1929, Birkhoff proved the existence of an entire function F on
with the property that for any entire function f there exists a sequence {ak} of complex numbers such that {F(ζ+ak)} converges to f (ζ) uniformly on compact sets. Luh proved a variant of Birkhoff's theorem and the second author proved a theorem analogous to that of Luh for the multiplicative group
*. In this paper extensions of the above results to the multi-dimensional case are proved. Let M(n,
) be the set of all square matrices of degree n with complex coefficients, and let G=GL(n,
) be the general linear group of degree n over
. We denote by
(G) the set of all holomorphic functions on G. Similarly, we define
(
). Let K be the
(G)-hull of a compact set K in G. Finally we denote by B(G) the set of all compact subsets K of G with K=K such that there exists a holomorphic function f on M(n,
) with f(0)(f(K)), where (f(K)) is the
(
)-hull of f(K). Our main result is the following. There exists a holomorphic function F on G such that for any KB(G), for any function f holomorphic in some neighbourhood of K, and for any >0, there exists CG with maxZK |F(CZ)−f(Z)|<. 相似文献
15.
Let , with
-1=x0n<x1n<<xnn<xn+1,n=1