共查询到20条相似文献,搜索用时 31 毫秒
1.
M. Brodmann 《Archiv der Mathematik》2002,79(2):87-92
Let M be a finitely generated faithful module over a noetherian ring R of dimension d < ¥ \infty and let \mathfrak a \subseteqq R {\mathfrak a} \subseteqq R be an ideal. We describe the (finite) set SuppR(H\mathfrak ad (M)) = AssR(H\mathfrak ad (M)) \textrm{Supp}_R(H_{\mathfrak a}^d (M)) = \textrm{Ass}_R(H_{\mathfrak a}^d (M)) of primes associated to the highest local cohomology module H\mathfrak ad (M) H_{\mathfrak a}^d (M) in terms of the local formal behaviour of \mathfrak a {\mathfrak a} . If R is integral and of finite type over a field, SuppR(H\mathfrak ad (M)) \textrm{Supp}_R(H_{\mathfrak a}^d (M)) is the set of those closed points of X = Spec(R) whose fibre under the normalization morphism n: X¢? X \nu : X' \rightarrow X contains points which are isolated in n-1(Spec(R/\mathfrak a)) \nu^{-1}(\textrm{Spec}(R/{\mathfrak a})) . 相似文献
2.
S. Reifferscheid 《Archiv der Mathematik》2000,75(3):164-172
Let \frak X, \frak F,\frak X\subseteqq \frak F\frak {X}, \frak {F},\frak {X}\subseteqq \frak {F}, be non-trivial Fitting classes of finite soluble groups such that G\frak XG_{\frak {X}} is an \frak X\frak {X}-injector of G for all G ? \frak FG\in \frak {F}. Then \frak X\frak {X} is called \frak F\frak {F}-normal. If \frak F=\frak Sp\frak {F}=\frak {S}_{\pi }, it is known that (1) \frak X\frak {X} is \frak F\frak {F}-normal precisely when \frak X*=\frak F*\frak {X}^{\ast }=\frak {F}^{\ast }, and consequently (2) \frak F í \frak X\frak N\frak {F}\subseteq \frak {X}\frak {N} implies \frak X*=\frak F*\frak {X}^{\ast }=\frak {F}^{\ast }, and (3) there is a unique smallest \frak F\frak {F}-normal Fitting class. These assertions are not true in general. We show that there are Fitting classes \frak F\not = \frak Sp\frak {F}\not =\frak {S}_{\pi } filling property (1), whence the classes \frak Sp\frak {S}_{\pi } are not characterized by satisfying (1). Furthermore we prove that (2) holds true for all Fitting classes \frak F\frak {F} satisfying a certain extension property with respect to wreath products although there could be an \frak F\frak {F}-normal Fitting class outside the Lockett section of \frak F\frak {F}. Lastly, we show that for the important cases \frak F=\frak Nn, n\geqq 2\frak {F}=\frak {N}^{n},\ n\geqq 2, and \frak F=\frak Sp1?\frak Spr, pi \frak {F}=\frak {S}_{p_{1}}\cdots \frak {S}_{p_{r}},\ p_{i} primes, there is a unique smallest \frak F\frak {F}-normal Fitting class, which we describe explicitly. 相似文献
3.
G. Kutyniok 《Archiv der Mathematik》2002,78(2):135-144
Let
r\mathbbR \rho_{\mathbb{R}} be the classical Schrödinger representation of the Heisenberg group and let L \Lambda be a finite subset of
\mathbbR ×\mathbbR \mathbb{R} \times \mathbb{R} . The question of when the set of functions
{t ? e2 pi y t f(t + x) = (r\mathbbR(x, y, 1) f)(t) : (x, y) ? L} \{t \mapsto e^{2 \pi i y t} f(t + x) = (\rho_{\mathbb{R}}(x, y, 1) f)(t) : (x, y) \in \Lambda\} is linearly independent for all
f ? L2(\mathbbR), f 1 0 f \in L^2(\mathbb{R}), f \neq 0 , arises from Gabor analysis. We investigate an analogous problem for locally compact abelian groups G. For a finite subset L \Lambda of G ×[^(G)] G \times \widehat{G} and rG \rho_G the Schrödinger representation of the Heisenberg group associated with G, we give a necessary and in many situations also sufficient condition for the set {rG (x, w, 1)f : (x, w) ? L} \{\rho_G (x, w, 1)f : (x, w) \in \Lambda\} to be linearly independent for all f ? L2(G), f 1 0 f \in L^2(G), f \neq 0 . 相似文献
4.
Suppose G is a transitive permutation group on a finite set W\mit\Omega of n points and let p be a prime divisor of |G||G|. The smallest number of points moved by a non-identity p-element is called the minimal p-degree of G and is denoted mp (G). ¶ In the article the minimal p-degrees of various 2-transitive permutation groups are calculated. Using the classification of finite 2-transitive permutation groups these results yield the main theorem, that mp(G) 3 [(p-1)/(p+1)] ·|W|m_{p}(G) \geq {{p-1} \over {p+1}} \cdot |\mit\Omega | holds, if Alt(W) \nleqq G {\rm Alt}(\mit\Omega ) \nleqq G .¶Also all groups G (and prime divisors p of |G||G|) for which mp(G) £ [(p-1)/(p)] ·|W|m_{p}(G)\le {{p-1}\over{p}} \cdot |\mit\Omega | are identified. 相似文献
5.
We will say that a subgroup X of G satisfies property C in G if CG(X?Xg)\leqq X?Xg{\rm C}_{G}(X\cap X^{{g}})\leqq X\cap X^{{g}} for all g ? G{g}\in G. We obtain that if X is a nilpotent subgroup satisfying property C in G, then XF(G) is nilpotent. As consequence it follows that if N\triangleleft GN\triangleleft G is nilpotent and X is a nilpotent subgroup of G then CG(N?X)\leqq XC_G(N\cap X)\leqq X implies that NX is nilpotent.¶We investigate the relationship between the maximal nilpotent subgroups satisfying property C and the nilpotent injectors in a finite group. 相似文献
6.
E. Decreux 《Archiv der Mathematik》2000,75(6):430-437
In this note, we examine the structure of closed ideals of a quasianalytic weighted Beurling algebra A\cal {A}. This algebra is contained in C¥ (G){\cal C}^\infty (\mit\Gamma) and contains the set A¥ (D)A^\infty (D). Like in a previous article (see [6]), we use division properties and we give a characterization of closed ideals I such that I?A¥ 1 { 0}I\cap A^\infty\! \ne \{ 0\} . Then, we use a factorization property proved in [2], which allows us to describe all the closed ideals of A\cal {A}. 相似文献
7.
K. W. Roggenkamp 《Archiv der Mathematik》2000,74(3):173-182
Let B\cal B be a p-block of cyclic defect of a Hecke order over the complete ring
\Bbb Z[q] áq-1,p ?\Bbb {Z}[q] _{\langle q-1,p \rangle}; i.e. modulo áq-1 ?\langle q-1 \rangle it is a p-block B of cyclic defect of the underlying Coxeter group G. Then B\cal B is a tree order over
\Bbb Z[q]áq-1, p ?\Bbb {Z}[q]_{\langle q-1, p \rangle } to the Brauer tree of B. Moreover, in case B\cal B is the principal block of the Hecke order of the symmetric group S(p) on p elements, then B\cal B can be described explicitly. In this case a complete set of non-isomorphic indecomposable Cohen-Macaulay B\cal B-modules is given. 相似文献
8.
A.A. Baranov 《Archiv der Mathematik》1999,72(2):101-106
An algebra is called finitary if it consists of finite-rank transformations of a vector space. We classify finitary simple Lie algebras over an algebraically closed field of zero characteristic. It is shown that any such algebra is isomorphic to one of the following¶ (1) a special transvection algebra
\frak t(V,P)\frak t(V,\mit\Pi );¶ (2) a finitary orthogonal algebra
\frak fso (V,q)\frak {fso} (V,q); ¶ (3) a finitary symplectic algebra
\frak fsp (V,s)\frak {fsp} (V,s).¶Here V is an infinite dimensional K-space; q (respectively, s) is a symmetric (respectively, skew-symmetric) nondegenerate bilinear form on V; and P\Pi is a subspace of the dual V* whose annihilator in V is trivial: 0={v ? V | Pv=0}0=\{{v}\in V\mid \Pi {v}=0\}. 相似文献
9.
J.-F. Quint 《Commentarii Mathematici Helvetici》2002,77(3):563-608
Soient G un groupe de Lie semi-simple, réel, connexe et de centre fini, \mathfrak a \mathfrak a un sous-espace de Cartan de lalgèbre de Lie de G et \mathfrak a+ ì \mathfrak a \mathfrak a^{+} \subset \mathfrak a une chambre de Weyl fermée de \mathfrak a \mathfrak a . Si G \Gamma est un sous-groupe discret Zariski dense de G, nous lui associons une fonction homogène yG : \mathfrak a+ ? \mathbb R è{-¥} \psi_{\Gamma} : \mathfrak a^{+} \rightarrow \mathbb {R} \cup \{-\infty\} qui généralise lexposant de convergence de G \Gamma considéré en \mathbb R \mathbb {R} -rang 1. Nous montrons alors que cette fonction est concave. Dans un travail ultérieur, nous en déduirons des constructions de généralisations des mesures de Patterson-Sullivan.¶ Nous démontrons aussi des analogues de nos résultats sur les corps locaux. 相似文献
10.
B. Enriquez 《Selecta Mathematica, New Series》2001,7(3):321-407
To any field
\Bbb K \Bbb K of characteristic zero, we associate a set
(\mathbbK) (\mathbb{K}) and a group
G0(\Bbb K) {\cal G}_0(\Bbb K) . Elements of
(\mathbbK) (\mathbb{K}) are equivalence classes of families of Lie polynomials subject to associativity relations. Elements of
G0(\Bbb K) {\cal G}_0(\Bbb K) are universal automorphisms of the adjoint representations of Lie bialgebras over
\Bbb K \Bbb K . We construct a bijection between
(\mathbbK)×G0(\Bbb K) (\mathbb{K})\times{\cal G}_0(\Bbb K) and the set of quantization functors of Lie bialgebras over
\Bbb K \Bbb K . This construction involves the following steps.? 1) To each element v \varpi of
(\mathbbK) (\mathbb{K}) , we associate a functor
\frak a?\operatornameShv(\frak a) \frak a\mapsto\operatorname{Sh}^\varpi(\frak a) from the category of Lie algebras to that of Hopf algebras;
\operatornameShv(\frak a) \operatorname{Sh}^\varpi(\frak a) contains
U\frak a U\frak a .? 2) When
\frak a \frak a and
\frak b \frak b are Lie algebras, and
r\frak a\frak b ? \frak a?\frak b r_{\frak a\frak b} \in\frak a\otimes\frak b , we construct an element
?v (r\frak a\frak b) {\cal R}^{\varpi} (r_{\frak a\frak b}) of
\operatornameShv(\frak a)?\operatornameShv(\frak b) \operatorname{Sh}^\varpi(\frak a)\otimes\operatorname{Sh}^\varpi(\frak b) satisfying quasitriangularity identities; in particular,
?v(r\frak a\frak b) {\cal R}^\varpi(r_{\frak a\frak b}) defines a Hopf algebra morphism from
\operatornameShv(\frak a)* \operatorname{Sh}^\varpi(\frak a)^* to
\operatornameShv(\frak b) \operatorname{Sh}^\varpi(\frak b) .? 3) When
\frak a = \frak b \frak a = \frak b and
r\frak a ? \frak a?\frak a r_\frak a\in\frak a\otimes\frak a is a solution of CYBE, we construct a series
rv(r\frak a) \rho^\varpi(r_\frak a) such that
?v(rv(r\frak a)) {\cal R}^\varpi(\rho^\varpi(r_\frak a)) is a solution of QYBE. The expression of
rv(r\frak a) \rho^\varpi(r_\frak a) in terms of
r\frak a r_\frak a involves Lie polynomials, and we show that this expression is unique at a universal level. This step relies on vanishing
statements for cohomologies arising from universal algebras for the solutions of CYBE.? 4) We define the quantization of a
Lie bialgebra
\frak g \frak g as the image of the morphism defined by ?v(rv(r)) {\cal R}^\varpi(\rho^\varpi(r)) , where
r ? \mathfrakg ?\mathfrakg* r \in \mathfrak{g} \otimes \mathfrak{g}^* .<\P> 相似文献
11.
Let ${\Gamma < {\rm SL}(2, {\mathbb Z})}Let
G < SL(2, \mathbb Z){\Gamma < {\rm SL}(2, {\mathbb Z})} be a free, finitely generated Fuchsian group of the second kind with no parabolics, and fix two primitive vectors
v0, w0 ? \mathbb Z2 \ {0}{v_{0}, w_{0} \in \mathbb {Z}^{2} \, {\backslash} \, \{0\}}. We consider the set S{\mathcal {S}} of all integers occurring in áv0g, w0?{\langle v_{0}\gamma, w_{0}\rangle}, for g ? G{\gamma \in \Gamma} and the usual inner product on
\mathbb R2{\mathbb {R}^2}. Assume that the critical exponent δ of Γ exceeds 0.99995, so that Γ is thin but not too thin. Using a variant of the circle method, new bilinear forms estimates
and Gamburd’s 5/6-th spectral gap in infinite-volume, we show that S{\mathcal {S}} contains almost all of its admissible primes, that is, those not excluded by local (congruence) obstructions. Moreover, we
show that the exceptional set
\mathfrak E(N){\mathfrak {E}(N)} of integers |n| < N which are locally admissible (n ? S (mod q) for all q 3 1){(n \in \mathcal {S} \, \, ({\rm mod} \, q) \, \, {\rm for\,all} \,\, q \geq 1)} but fail to be globally represented, n ? S{n \notin \mathcal {S}}, has a power savings,
|\mathfrak E(N)| << N1-e0{|\mathfrak {E}(N)| \ll N^{1-\varepsilon_{0}}} for some ${\varepsilon_{0} > 0}${\varepsilon_{0} > 0}, as N → ∞. 相似文献
12.
Takuro Fukunaga 《Graphs and Combinatorics》2011,27(5):647-659
An undirected graph G = (V, E) is called
\mathbbZ3{\mathbb{Z}_3}-connected if for all
b: V ? \mathbbZ3{b: V \rightarrow \mathbb{Z}_3} with ?v ? Vb(v)=0{\sum_{v \in V}b(v)=0}, an orientation D = (V, A) of G has a
\mathbbZ3{\mathbb{Z}_3}-valued nowhere-zero flow
f: A? \mathbbZ3-{0}{f: A\rightarrow \mathbb{Z}_3-\{0\}} such that ?e ? d+(v)f(e)-?e ? d-(v)f(e)=b(v){\sum_{e \in \delta^+(v)}f(e)-\sum_{e \in \delta^-(v)}f(e)=b(v)} for all v ? V{v \in V}. We show that all 4-edge-connected HHD-free graphs are
\mathbbZ3{\mathbb{Z}_3}-connected. This extends the result due to Lai (Graphs Comb 16:165–176, 2000), which proves the
\mathbbZ3{\mathbb{Z}_3}-connectivity for 4-edge-connected chordal graphs. 相似文献
13.
Let G be a finite soluble group and
F\mathfrakX(G) {\Phi_\mathfrak{X}}(G) an intersection of all those maximal subgroups M of G for which
G