共查询到10条相似文献,搜索用时 125 毫秒
1.
Richter 《Discrete and Computational Geometry》2002,28(3):427-442
Let G be a group of affine transformations of the plane R 2 and let the family F consist of all topological discs in R 2 whose boundary is subject to some smoothness condition (general, rectifiable, piecewise C 1 , piecewise C 2 ). Are any two members D,E ∈ F congruent by dissection with respect to G such that all the pieces in the corresponding dissections of D and E belong to F as well? We give an affirmative answer if G contains all affine transformations and F consists of the discs whose boundary is piecewise C 1 . An example shows that C 1 cannot be replaced by C 2 . Moreover, if G is either the group of equiaffine transformations or the group of similarities, then congruence by dissection of two convex discs D and E turns out to be essentially equivalent to congruence by dissection of the boundaries bd(D ) and bd(E ). 相似文献
2.
Summary Let Fn, n≧ 1, denote the sequence of generic filiform (connected, simply connected) Lie groups. Here we study, for each Fn, the infinite dimensional simple quotients of the group C*-algebra of (the most obvious) one of its discrete cocompact subgroups Dn. For Dn, the most attractive concrete faithful representations are given in terms of Anzai flows, in analogy with the representations
of the discrete Heisenberg group H3 ⊆G3 on L2(T) that result from the irrational rotation flows on T; the representations of Dn generate infinite-dimensional simple quotients An,θ of the group C*-algebra C*(Dn). For n>1, there are other infinite-dimensional simple quotients of C*(Dn) arising from non-faithful representations of Dn. Flows for these are determined, and they are also characterized and represented as matrix algebras over simple affine Furstenberg
transformation group C*-algebras of the lower dimensional tori. 相似文献
3.
We give sufficient conditions for a differential equation to have a given semisimple group as its Galois group. For any group G with G 0 = G 1 · ··· · G r , where each G i is a simple group of type A?, C?, D?, E6, or E7, we construct a differential equation over C(x) having Galois group G. 相似文献
4.
Emmanuel Peyre 《Inventiones Mathematicae》2008,171(1):191-225
Let G be a finite group and W be a faithful representation of G over C. The group G acts on the field of rational functions C(W). The question whether the field of invariant functions C(W)
G
is purely transcendental over C goes back to Emmy Noether. Using the unramified cohomology group of degree 2 of this field as an invariant, Saltman gave
the first examples for which C(W)
G
is not rational over C. Around 1986, Bogomolov gave a formula which expresses this cohomology group in terms of the cohomology of the group G.
In this paper, we prove a formula for the prime to 2 part of the unramified cohomology group of degree 3 of C(W)
G
. Specializing to the case where G is a central extension of an F
p
-vector space by another, we get a method to construct nontrivial elements in this unramified cohomology group. In this way
we get an example of a group G for which the field C(W)
G
is not rational although its unramified cohomology group of degree 2 is trivial.
Dedicated to Jean-Louis Colliot-Thélène. 相似文献
5.
Guyan Robertson 《K-Theory》2004,33(4):347-369
Let (G, I, N, S) be an affine topological Tits system, and let Γ be a torsion-free cocompact lattice in G. This article studies the coinvariants H
0(Γ; C(Ω,Z)), where Ω is the Furstenberg boundary of G. It is shown that the class [1] of the identity function in H
0(Γ; C(Ω, Z)) has finite order, with explicit bounds for the order. A similar statement applies to the K
0 group of the boundary crossed product C
*-algebra C(Ω)Γ. If the Tits system has type ?
2, exact computations are given, both for the crossed product algebra and for the reduced group C
*-algebra. 相似文献
6.
If the additive group of complex numbers acts algebraically on a normal affine variety, then the associated ring of invariants need not be finitely generated, but is an ideal transform of some normal affine algebra (Theorem 1). We investigate such normal affine algebras in the case of a locally trivial action on a factorial variety. If the variety is a complex affine space and the ring of invariants is isomorphic to a polynomial ring, then the action is conjugate to a translation (Theorem 3). Equivalently, ifC
n
, is the total space for a principalG
a
-bundle over some open subset ofC
n–1 then the bundle is trivial. On the other hand, there is a locally trivialG
a
-action on a normal affine variety with nonfinitely generated ring of invariants (Theorem 2).Supported in part by NSA Grant No. MDA904-96-1-0069 相似文献
7.
《代数通讯》2013,41(8):3559-3570
This paper concerns some of the conditions satisfied by additive group actions on complex affine space which can be written locally as a translation of a variable. Assume X is the affine variety C n , Ga = (C, +), and σ : Ga × X → X is the action defined by a group monomorphism G a → Aut C X. If σ is locally trivial, then the action satisfies what is termed a “GICO” condition. It will be shown that a large class of Ga -actions on C 4, that is, fixed-point free, “twin-triangular” actions with finitely-generated rings of invariants, are at least GICO. Remaining questions are discussed. 相似文献
8.
《代数通讯》2013,41(9):3367-3373
ABSTRACT Let D be a finite dimensional F -central division algebra and G an irreducible subgroup of D*: = GL 1(D). Here we investigate the structure of D under various group identities on G. In particular, it is shown that when [D:F] = p 2, p a prime, then D is cyclic if and only if D* contains a nonabelian subgroup satisfying a group identity. 相似文献
9.
Christian Richter 《Journal of Geometry》2006,84(1-2):117-132
Let
be a group of affine transformations of the Euclidean plane
. Two topological discs D,
are called congruent by dissection with respect to
if D can be dissected into a finite number of subdiscs that can be rearranged by maps from
to a dissection of E.
Our main result says in particular that
admits congruence by dissection of any circular disc C with any square S if and only if
contains a contractive map and all orbits
,
, are dense in
. In this case any two discs D and E are congruent by dissection with respect to
and every disc D is congruent by dissection with n copies of D for every n ≥ 2.
Moreover, we give estimates on minimal numbers of pieces that are needed to realize congruences by dissection.
Dedicated to Irmtraud Stephani on the occasion of her 70th birthday 相似文献
10.
LetG=GL(m, D) whereD is a central division algebra over a commutative nonarchimedean local fieldF. LetE/F be a field extension contained inM(m, D). We denote byI (resp.I
E) the nonextended affine building ofG (resp. of the centralizer ofE
x inG). In this paper we prove that there exists a uniqueG
E-equivariant affine mapj
EIEI. It is injective and its image coincides with the set ofE
x-fixed points inI. Moreover, we prove thatj
E is compatible with the Moy-Prasad filtrations.This author's contribution was written while he was a post-doctoral student at King's College London and supported by an european TMR grant 相似文献