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1.
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
2.
Paul Levy 《Journal of Algebra》2002,250(2):473
Let K be an algebraically closed field of positive characteristic and let G be a reductive group over K with Lie algebra
. This paper will show that under certain mild assumptions on G, the commuting variety
(
) is an irreducible algebraic variety. 相似文献
3.
G. A. Soifer 《Journal of Algebra》2002,250(2):647
Let
n be a Euclidean space and let S be a Euclidean semigroup, i.e., a subsemigroup of the group of isometries of
n. We say that a semigroup S acts discontinuously on
n if the subset {s S:sK ∩ K ≠ } is finite for any compact set K of
n. The main results of this work areTheorem.If S is a Euclidean semigroup which acts discontinuously on
n, then the connected component of the closure of the linear part ℓ(S) of S is a reducible group.Corollary.Let S be a Euclidean semigroup acting discontinuously on
n; then the linear part ℓ(S) of S is not dense in the orthogonal group O(n).These results are the first step in the proof of the followingMargulis' Conjecture.If S is a crystallographic Euclidean semigroup, then S is a group. 相似文献
4.
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
5.
Raymundo Bautista William Crawley-Boevey Tiangang Lei Yingbo Zhang 《Journal of Algebra》2000,230(2):665
In the present paper we prove that a certain subcategory
of the module category over some infinite-dimensional algebra R has almost split sequences and strongly homogeneous property; i.e., for each indecomposable module M in
, there is an almost split sequence starting and also ending at M. It is also proved that except for a trivial case,
is of wild representation type. 相似文献
6.
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
7.
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
8.
Nicholas Hanges 《Journal of Functional Analysis》2004,210(2):295-320
We study a partial differential operator
with analytic coefficients, which is of the form “sum of squares”.
is hypoelliptic on any open subset of
, yet possesses the following properties: (1)
is not analytic hypoelliptic on any open subset of
that contains 0. (2) If u is any distribution defined near
with the property that
is analytic near 0, then u must be analytic near 0. (3) The point 0 lies on the projection of an infinite number of Treves curves (bicharacteristics).These results are consistent with the Treves conjectures. However, it follows that the analog of Treves conjecture, in the sense of germs, is false.As far as we know,
is the first example of a “sum of squares” operator which is not analytic hypoelliptic in the usual sense, yet is analytic hypoelliptic in the sense of germs. 相似文献
9.
Larry Smith 《Finite Fields and Their Applications》2002,8(4):504
Let
q be the finite field with q elements, q=pν, p
a prime, and Mat2.2(
q) the vector space of 2×2-matrices over
. The group GL(2,
) acts on Mat2,2(
q) by conjugation. In this note, we determine the invariants of this action. In contrast to the case of an infinite field, where the trace and determinant generate the ring of invariants, several new invariants appear in the case of finite fields. 相似文献
10.
Let Ω be a region in the complex plane. In this paper we introduce a class of sesquianalytic reproducing kernels on Ω that we call B-kernels. When Ω is the open unit disk
and certain natural additional hypotheses are added we call such kernels k Bergman-type kernels. In this case the associated reproducing kernel Hilbert space
(k) shares certain properties with the classical Bergman space L2α of the unit disk. For example, the weighted Bergman kernels kβw(z)=(1−wz)−β, 1β2 are Bergman-type kernels. Furthermore, for any Bergman-type kernel k one has H2
(k)L2a, where the inclusion maps are contractive, and Mζ, the operator of multiplication with the identity function ζ, defines a contraction operator on
(k). Our main results about Bergman-type kernels k are the following two: First, once properly normalized, the reproducing kernel for any nontrivial zero based invariant subspace
of
(k) is a Bergman-type kernel as well. For the weighted Bergman kernels kβ this result even holds for all
ζ-invariant subspace
of index 1, i.e., whenever the dimension of
/ζ
is one. Second, if
is any multiplier invariant subspace of
(k), and if we set
*=
z
, then Mζ
is unitarily equivalent to Mζ acting on a space of
*-valued analytic functions with an operator-valued reproducing kernel of the type
where V is a contractive analytic function V :
→
(
,
*), for some auxiliary Hilbert space
. Parts of these theorems hold in more generality. Corollaries include contractive divisor, wandering subspace, and dilation theorems for all Bergman-type reproducing kernel Hilbert spaces. When restricted to index one invariant subspaces of
(kβ), 1β2, our approach yields new proofs of the contractive divisor property, the strong contractive divisor property, and the wandering subspace theorems and inner–outer factorization. Our proofs are based on the properties of reproducing kernels, and they do not involve the use of biharmonic Green functions as had some of the earlier proofs. 相似文献
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11.
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
12.
Replacing invertibility with quasi-invertibility in Bass' first stable range condition we discover a new class of rings, the QB-rings. These constitute a considerable enlargement of the class of rings with stable rank one (B-rings) and include examples like End
(V), the ring of endomorphisms of a vector space V over some field
, and
(
), the ring of all row- and column-finite matrices over
. We show that the category of QB-rings is stable under the formation of corners, ideals, and quotients, as well as matrices and direct limits. We also give necessary and sufficient conditions for an extension of QB-rings to be a QB-ring, and show that extensions of B-rings often lead to QB-rings. Specializing to the category of exchange rings we characterize the subset of exchange QB-rings as those in which every von Neumann regular element extends to a maximal regular element, i.e., a quasi-invertible element. Finally we show that the C*-algebras that are QB-rings are exactly the extremally rich C*-algebras studied by L. G. Brown and the second author. 相似文献
13.
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
14.
Given an (n+1)-dimensional space
of piecewise smooth functions in which each basis has a non-vanishing Wronskian, and its dual space
*, a canonical bilinear form is defined on
×
*, which provides a simple characterization of a contact of order rn. An intrinsic reproducing function is introduced, leading to Marsden-type identities. In the case of Chebyshev spaces connected with totally positive matrices, the bilinear form yields a general notion of blossom which can be extended to Chebyshev splines. 相似文献
15.
Let f(x) be a strongly primitive polynomial of degree n over Z/(2e), η(x0,x1,…,xe−2) a Boolean function of e−1 variables and (x0,x1,…,xe−1)=xe−1+η(x0,x1,…,xe−2)G (f(x),Z/(2e)) denotes the set of all sequences over Z/(2e) generated by f(x), F2∞ the set of all sequences over the binary field F2, then the compressing mapping
is injective, that is, for
,
G(f(x),Z/(2e)),
=
if and only if Φ(
)=Φ(
), i.e., (
0,…,
e−1)=(
0,…,
e−1) mod 2. In the second part of the paper, we generalize the above result over the Galois rings. 相似文献
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16.
Given an algebraic theory
whose category of models is semi-abelian, we study the category
of topological models of
and generalize to it most classical results on topological groups. In particular,
is homological, which includes Barr regularity and forces the Mal'cev property. Every open subalgebra is closed and every quotient map is open. We devote special attention to the Hausdorff, compact, locally compact, connected, totally disconnected and profinite
-algebras. 相似文献
17.
Binary decision diagrams are in widespread use in verification systems for the canonical representation of finite functions. Here we consider multivalued BDDs, which represent functions of the form :
ν →
, where
is a finite set of leaves. We study a rather natural online BDD refinement problem: a partition of the leaves of several shared BDDs is gradually refined, and the equivalence of the BDDs under the current partition must be maintained in a discriminator table. We show that it can be solved in O(n log n) time if n bounds both the size of the BDDs and the total size of update operations. Our algorithm is based on an understanding of BDDs as the fixed points of an operator that in each step splits and gathers nodes. We apply our algorithm to show that automata BDD-represented transition functions can be minimized in time O(n · log n), where n is the total number of BDD nodes representing the automaton. This result is not an instance of Hopcroft's classical minimization algorithm, which breaks down for BDD-represented automata because of the BDD path compression property. 相似文献
18.
University of Georgia VIGRE Algebra Group 《Journal of Algebra》2004,280(2):371
Let G be a simple algebraic group over k=C, or where p is good. Set g=LieG. Given rN and a faithful (restricted) representation , one can define a variety of nilpotent elements . In this paper we determine this variety when ρ is an irreducible representation of minimal dimension or the adjoint representation. 相似文献
19.
A. Bir 《Indagationes Mathematicae》2000,11(4):499
Let z1, z2, …, zn be complex numbers, and write
for their power sums. Let
where the minimum is taken under the condition that
. In this paper we prove that
. 相似文献
20.
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