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1.
The subgroups E(m,R) ⊗ E(n,R) ≤ H ≤ G = GL(mn,R) are studied under the assumption that the ring R is commutative and m, n ≥ 3. The group GL
m
⊗GL
n
is defined by equations, the normalizer of the group E(m,R) ⊗ E(n,R) is calculated, and with each intermediate subgroup H it is associated a uniquely determined lower level (A,B,C), where A,B,C are ideals in R such that mA,A
2 ≤ B ≤ A and nA,A
2 ≤ C ≤ A. The lower level specifies the largest elementary subgroup satisfying the condition E(m, n,R, A,B,C) ≤ H. The standard answer to this problem asserts that H is contained in the normalizer N
G
(E(m,n,R, A,B,C)). Bibliography: 46 titles. 相似文献
2.
Arrangements and cohomology 总被引:11,自引:0,他引:11
Michael Falk 《Annals of Combinatorics》1997,1(1):135-157
3.
We consider random systems generated by two-sided compositions of random surface diffeomorphisms,together with an ergodic Borel probability measure μ.Let D(μω)be its dimension of the sample measure,then we prove a formula relating D(μω)to the entropy and Lyapunov exponents of the random system,where D(μω)is dimHμω,-/dinBμω,or-/dimBμω. 相似文献
4.
Leonid A. Kurdachenko Alexey V. Sadovnichenko Igor Ya. Subbotin 《Central European Journal of Mathematics》2010,8(2):261-265
Let F be a field, A be a vector space over F, GL(F, A) be the group of all automorphisms of the vector space A. A subspace B of A is called nearly G-invariant, if dim
F
(BFG/B) is finite. A subspace B is called almost G-invariant, if dim
F
(B/Core
G
(B)) is finite. In the current article, we study linear groups G such that every subspace of A is either nearly G-invariant or almost G-invariant in the case when G is a soluble p-group where p = char
F. 相似文献
5.
6.
Let F be a non-Archimedean local field whose residue characteristic is odd. In this paper we develop a theory of newforms
forU (1, 1)(F), building on previous work onSL
2(F). This theory is analogous to the results of Casselman forGL
2(F) and Jacquet, Piatetski-Shapiro, and Shalika forGL
n(F). To a representation π ofU(1, 1)(F), we attach an integer c(π) called the conductor of π, which depends only on theL-packet π containing π. A newform is a vector in π which is essentially fixed by a congruence subgroup of level c(π). We show
that our newforms are always test vectors for some standard Whittaker functionals, and, in doing so, we give various explicit
formulae for newforms. 相似文献
7.
Under a general hypothesis an expanding map T of a Riemannian manifold M is known to preserve a measure equivalent to the Liouville measure on that manifold. As a consequence of this and Birkhoff’s
pointwise ergodic theorem, the orbits of almost all points on the manifold are asymptotically distributed with regard to this
Liouville measure. Let T be Lipschitz of class τ for some τ in (0,1], let Ω(x) denote the forward orbit closure of x and for a positive real number δ and let E(x0, δ) denote the set of points x in M such that the distance from x0 to Ω is at least δ. Let dim A denote the Hausdorff dimension of the set A. In this paper we prove a result which implies that there is a constant C(T) > 0 such that
dimE(x0,d) 3 dimM - \fracC(T)|logd| \dim E(x_0,\delta) \ge \dim M - \frac{C(T)}{\vert\!\log \delta \vert}
if τ = 1 and
dimE(x0,d) 3 dimM - \fracC(T)log|logd|\dim E(x_0,\delta) \ge \dim M - \frac{C(T)}{\log \vert \log \delta \vert}
if τ < 1. This gives a quantitative converse to the above asymptotic distribution phenomenon. The result we prove is of sufficient
generality that a similar result for expanding hyperbolic rational maps of degree not less than two follows as a special case. 相似文献
8.
Quanshui Wu 《Israel Journal of Mathematics》1991,73(3):289-296
LetF ⊂K be a field extension,A be aK-algebra. It is proved that, in general, GK dim
F
A≥GK dim
K
A+tr
F
(K). For commutative algebras or Noetherian P.I. algebras, the equality holds. Two examples are also constructed to show that:
(i) there exists an algebraA such that GK dim
F
A=GK dim
K
A+tr
F
(K)+1; (ii) there exists an algebraic extensionF ⊂K and aK-algebraA such that GK dim
F
A=∞, but GK dim
K
A<∞. 相似文献
9.
Let G = GL
N
or SL
N
as reductive linear algebraic group over a field k of characteristic p > 0. We prove several results that were previously established only when N ⩽ 5 or p > 2
N
: Let G act rationally on a finitely generated commutative k-algebra A and let grA be the Grosshans graded ring. We show that the cohomology algebra H
*(G, grA) is finitely generated over k. If moreover A has a good filtration and M is a Noetherian A-module with compatible G action, then M has finite good filtration dimension and the H
i
(G, M) are Noetherian A
G
-modules. To obtain results in this generality, we employ functorial resolution of the ideal of the diagonal in a product
of Grassmannians. 相似文献
10.
W. M. Mikulski 《Czechoslovak Mathematical Journal》2011,61(1):157-168
Let F = F
(A,H,t) and F1 = F(A1,H1,t1){F^1} = {F^{({A^1},{H^1},{t^1})}} be fiber product preserving bundle functors on the category FM
m
of fibred manifolds Y with m-dimensional bases and fibred maps covering local diffeomorphisms. We define a quasi-morphism (A, H, t) → (A
1, H
1, t
1) to be a GL(m)-invariant algebra homomorphism ν: A → A
1 with t
1 = ν ∘ t. The main result is that there exists an FM
m
-natural transformation FY → F
1
Y depending on a classical linear connection on the base of Y if and only if there exists a quasi-morphism (A, H, t) → (A
1, H
1, t
1). As applications, we study existence problems of symmetrization (holonomization) of higher order jets and of holonomic prolongation
of general connections. 相似文献
11.
Leonid A. Kurdachenko Alexey V. Sadovnichenko Igor Ya. Subbotin 《Central European Journal of Mathematics》2009,7(2):176-185
Let F be a field, A be a vector space over F, and GL(F,A) the group of all automorphisms of the vector space A. A subspace B of A is called nearly G-invariant, if dim
F
(BFG/B) is finite. A subspace B is called almost G-invariant, if dim
F
(B/Core
G
(B)) is finite. In the present article we begin the study of subgroups G of GL(F,A) such that every subspace of A is either nearly G-invariant or almost G-invariant. More precisely, we consider the case when G is a periodic p′-group where p = charF.
相似文献
12.
Leonid A. Kurdachenko Jose M. Muñoz-Escolano Javier Otal Nicolaj N. Semko 《Geometriae Dedicata》2009,138(1):69-81
Let F be a field and V a vector space over F. If G is a subgroup of GL(V, F), then we define the central dimension of
G (denoted by centdim
F
G) as the F-dimension of the factor-space V/C
V
(G). In this paper, we continue the study of locally nilpotent linear groups satisfying the weak minimal or the weak maximal
condition on their subgroups of infinite central dimension started in Kurdachenko et al. (Publ Mat 52:151–169, 2008).
Supported by Proyecto MTM2007-60994 of Dirección General de Investigación MEC (Spain). 相似文献
13.
Joachim Breitner 《Israel Journal of Mathematics》2012,191(2):545-557
For a representative class of subgroups of F r , the image of their stabilizer subgroup under the action of Aut(F r ) in GL r (ℤ) is calculated. 相似文献
14.
We look at a special case of a familiar problem: Given a locally compact group G, a subgroup H and a complex representation π+ of G how does π+ decompose on restriction to H. Here G is GL+(2,F), where F is a nonarchimedian local field of characteristic not two, K a separable quadratic extension of F, GL+(2,F) the subgroup of index 2 in GL(2,F) consisting of those matrices whose determinant is in NK/F(K∗), π+ is an irreducible, admissible supercuspidal representation of GL+(2,F) and H=K∗ under an embedding of K∗ into GL(2,F). 相似文献
15.
Let F be a non-Archimedean locally compact field, and let p be its residual characteristic. Put G=GL
p
(F) and let G
′=D
×, where $D$ is a division algebra with centre F and of degree p
2 over F. The Jacquet–Langlands correspondence is a bijection between the discrete series of G and that of G
′. We describe this explicitly, in terms of Carayol's parametrization of these discrete series.
Received: 25 November 1999 相似文献
16.
Let X be a compact complex homogeneous manifold and let Aut(X) be the complex Lie group of holomorphic automorphisms of X. It is well-known that the dimension of Aut(X) is bounded by an integer that depends only on n=dim
X. Moreover, if X is K?hler then dimAut (X)≤n(n+2) with equality only when X is complex projective space. In this article examples of non-K?hler compact complex homogeneous manifolds X are given that demonstrate dimAut(X) can depend exponentially on n.
Let X be a connected compact complex manifold of dimension n. The group of holomorphic automorphisms of X, Aut(X), is a complex Lie group [3]. For a fixed n>1, the dimension of Aut(X) can be arbitrarily large compared to n. Simple examples are provided by the Hirzebruch surfaces F
m
, m∈N, for which dimAut(F
m
)=m+5, see, e.g. [2, Example 2.4.2].
If X is homogeneous, that is, any point of X can be mapped to any other point of X under a holomorphic automorphism, then the dimension of the automorphism group of X is bounded by an integer that depends only on n, see [1, 2, 6]. The estimate given in [2, Theorem 3.8.2] is roughly dimAut(X)≤(n+2)
n
. For many classes of manifolds, however, the dimension of the automorphism group never exceeds n(n+2). For example, it follows directly from the classification given by Borel and Remmert [4], that if X is a compact homogeneous K?hler manifold, then dimAut(X)≤n(n+2) with equality only when X is complex projective space P
n
. It is an old question raised by Remmert, see [2, p. 99], [6], whether this same bound applies to all compact complex homogeneous
manifolds.
In this note we show that this is not the case by constructing non-K?hler compact complex homogeneous manifolds whose automorphism
group has a dimension that depends exponentially on n. The simplest case among these examples has n=3m+1 and dimAut(X)=3m+3
m
, so the above conjectured bound is exceeded when n≥19. These manifolds have the structure of non-trivial fiber bundles over products of flag manifolds with parallelizable fibers
given as the quotient of a solvable group by a discrete subgroup. They are constructed using the original ideas of Otte [6,
7] and are surprisingly similar to examples found there. Generally, a product of manifolds does not result in an automorphism
group with a large dimension relative to n. Nevertheless, products are used in an essential way in the construction given here, and it is perhaps this feature that
caused such examples to be previously overlooked.
Oblatum 13-X-97 & 24-X-1997 相似文献
17.
Let G
1 and G
2 be locally compact groups and let ω
1 and ω
2 be weight functions on G
1 and G
2, respectively. For i = 1, 2, let also C
0(G
i
, 1/ω
i
) be the algebra of all continuous complex-valued functions f on G
i
such that f/ω
i
vanish at infinity, and let H: C
0(G
1, 1/ω
1) → C
0(G
2, 1/ω
2) be a separating map; that is, a linear map such that H(f)H(g) = 0 for all f, g ∈ C
0(G
1, 1/ω
1) with fg = 0. In this paper, we study conditions under which H can be represented as a weighted composition map; i.e., H(f) = φ(f ℴ h) for all f ∈ C
0(G
1, 1/ω
1), where φ: G
2 → ℂ is a non-vanishing continuous function and h: G
2 → G
1 is a topological isomorphism. Finally, we offer a statement equivalent to that h is also a group homomorphism. 相似文献
18.
Let F n be the free group of rank n, and let Aut+(F n ) be its special automorphism group. For an epimorphism π : F n → G of the free group F n onto a finite group G we call the standard congruence subgroup of Aut+(F n ) associated to G and π. In the case n = 2 we fully describe the abelianization of Γ+(G, π) for finite abelian groups G. Moreover, we show that if G is a finite non-perfect group, then Γ+(G, π) ≤ Aut+(F 2) has infinite abelianization. 相似文献
19.
Behrooz Mirzaii 《Mathematische Annalen》2008,340(1):159-184
The homology of GL
n
(R) and SL
n
(R) is studied, where R is a commutative ‘ring with many units’. Our main theorem states that the natural map H
4(GL3(R), k) → H
4(GL4(R), k) is injective, where k is a field with char(k) ≠ 2, 3. For an algebraically closed field F, we prove a better result, namely, is injective. We will prove a similar result replacing GL by SL. This is used to investigate the indecomposable part of the
K-group K
4(R). 相似文献
20.
Let F be a non-Archimedean local field of residual characteristic two and let d be an odd positive integer. Let D be a central F-division algebra of dimension d
2. Let π be one of: an irreducible smooth representation of D
× , an irreducible cuspidal representation of GL
d
(F), an irreducible smooth representation of the Weil group of F of dimension d. We show that, in all these cases, if π is self-contragredient then it is defined over
\mathbb Q{\mathbb Q} and is orthogonal. We also show that such representations exist. 相似文献