共查询到20条相似文献,搜索用时 854 毫秒
1.
2.
L. Sanguiao Sande 《Geometriae Dedicata》2011,151(1):305-321
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4.
Christoph Lienau 《Mathematische Annalen》2011,351(2):403-410
For a real linear algebraic group G let A(G){\mathcal{A}(G)} be the algebra of analytic vectors for the left regular representation of G on the space of superexponentially decreasing functions. We present an explicit Dirac sequence in A(G){\mathcal{A}(G)}. Since A(G){\mathcal{A}(G)} acts on E for every Fréchet-representation (π, E) of moderate growth, this yields an elementary proof of a result of Nelson that the space of analytic vectors is dense in
E. 相似文献
5.
Carlo Alberto De Bernardi 《Archiv der Mathematik》2009,93(4):369-378
A selection theorem concerning support points of convex sets in a Banach space is proved. As a corollary we obtain the following result. Denote by ${\mathcal{BCC}(X)}A selection theorem concerning support points of convex sets in a Banach space is proved. As a corollary we obtain the following
result. Denote by BCC(X){\mathcal{BCC}(X)} the metric space of all nonempty bounded closed convex sets in a Banach space X. Then there exists a continuous mapping S : BCC(X) ? X{S : \mathcal{BCC}(X) \rightarrow X} such that S(K) is a support point of K for each K ? BCC(X){K \in \mathcal{BCC}(X)}. Moreover, it is possible to prescribe the values of S on a closed discrete subset of BCC(X){\mathcal{BCC}(X)}. 相似文献
6.
Let G be an archimedean ℓ-group and
\mathfrakP(G){\mathfrak{P}(G)} denote the set of all polar preserving bounded group endomorphisms of G. Bigard and Keimel in [Bull. Soc. Math. France 97 (1969), 381–398] and, independently, Conrad and Diem in [Illinois J. Math.
15 (1971), 222–240] proved that
\mathfrakP(G){\mathfrak{P}(G)} is an archimedean ℓ-group with respect to the pointwise addition and ordering. This classical result is extended in this
paper to certain sets of disjointness preserving bounded homomorphisms on archimedean ℓ-groups. 相似文献
7.
Taylor Series in Hermitean Clifford Analysis 总被引:1,自引:0,他引:1
In this paper, we consider the Taylor decomposition for h-monogenic functions in Hermitean Clifford analysis. The latter is to be considered as a refinement of the classical orthogonal
function theory, in which the structure group underlying the equations is reduced from
\mathfrakso(2m){\mathfrak{so}(2m)}to the unitary Lie algebra u(m). 相似文献
8.
9.
Let p be an odd prime and S a finite p-group. B. Oliver’s conjecture arises from an open problem in the theory of p-local finite groups. It is the claim that a certain characteristic subgroup
\mathfrakX(S){\mathfrak{X}(S)} of S always contains the Thompson subgroup. In previous work the first two authors and M. Lilienthal recast Oliver’s conjecture
as a statement about the representation theory of the factor group
S/\mathfrakX(S){S/\mathfrak{X}(S)}. We now verify the conjecture for a wide variety of groups
S/\mathfrakX(S){S/\mathfrak{X}(S)}. 相似文献
10.
Hung P. Tong-Viet 《Monatshefte für Mathematik》2012,15(2):559-577
Let G be a finite group. Denote by Irr(G) the set of all irreducible complex characters of G. Let cd(G)={c(1) | c ? Irr(G)}{{\rm cd}(G)=\{\chi(1)\;|\;\chi\in {\rm Irr}(G)\}} be the set of all irreducible complex character degrees of G forgetting multiplicities, and let X1(G) be the set of all irreducible complex character degrees of G counting multiplicities. Let H be any non-abelian simple exceptional group of Lie type. In this paper, we will show that if S is a non-abelian simple group and cd(S) í cd(H){{\rm cd}(S)\subseteq {\rm cd}(H)} then S must be isomorphic to H. As a consequence, we show that if G is a finite group with X1(G) í X1(H){{\rm X}_1(G)\subseteq {\rm X}_1(H)} then G is isomorphic to H. In particular, this implies that the simple exceptional groups of Lie type are uniquely determined by the structure of their complex group algebras. 相似文献
11.
Wojciech Jaworski 《Monatshefte für Mathematik》2008,336(4):135-144
Given a locally compact group G, let
J(G){\cal J}(G)
denote the set of closed left ideals in L
1(G), of the form J
μ = [L1(G) * (δ
e
− μ)]−, where μ is a probability measure on G. Let
Jd(G)={\cal J}_d(G)=
{Jm;m is discrete}\{J_{\mu};\mu\ {\rm is discrete}\}
,
Ja(G)={Jm;m is absolutely continuous}{\cal J}_a(G)=\{J_{\mu};\mu\ {\rm is absolutely continuous}\}
. When G is a second countable [SIN] group, we prove that
J(G)=Jd(G){\cal J}(G)={\cal J}_d(G)
and that
Ja(G){\cal J}_a(G)
, being a proper subset of
J(G){\cal J}(G)
when G is nondiscrete, contains every maximal element of
J(G){\cal J}(G)
. Some results concerning the ideals J
μ in general locally compact second countable groups are also obtained. 相似文献
12.
Benjamin Newton 《Archiv der Mathematik》2011,96(6):501-506
For a finite solvable group G and prime number p, we use elementary methods to obtain an upper bound for
\mathfrak mp(G){\mathfrak {m}_{p}(G)} , defined as the number of maximal subgroups of G whose index in G is a power of p. From this we derive an upper bound on the total number of maximal subgroups of a finite solvable group in terms of its order.
This bound improves existing bounds, and we identify conditions on the order of a finite solvable group under which this bound
is best possible. 相似文献
13.
In the first part of the paper we introduce the theory of bundles with negatively curved fibers. For a space X there is a forgetful map F X between bundle theories over X, which assigns to a bundle with negatively curved fibers over X its subjacent smooth bundle. Our main result states that, for certain k-spheres ${\mathbb{S}^k}In the first part of the paper we introduce the theory of bundles with negatively curved fibers. For a space X there is a forgetful map F
X
between bundle theories over X, which assigns to a bundle with negatively curved fibers over X its subjacent smooth bundle. Our main result states that, for certain k-spheres
\mathbbSk{\mathbb{S}^k}, the forgetful map
F\mathbbSk{F_{\mathbb{S}^k}} is not one-to-one. This result follows from Theorem A, which proves that the quotient map MET sec < 0 (M)?T sec < 0 (M){\mathcal{MET}^{\,\,sec <0 }(M)\rightarrow\mathcal{T}^{\,\,sec <0 }(M)} is not trivial at some homotopy levels, provided the hyperbolic manifold M satisfies certain conditions. Here MET sec < 0 (M){\mathcal{MET}^{\,\,sec <0 }(M)} is the space of negatively curved metrics on M and T sec < 0 (M) = MET sec < 0 (M)/ DIFF0(M){\mathcal{T}^{\,\,sec <0 }(M) = \mathcal{MET}^{\,\,sec <0 }(M)/ {\rm DIFF}_0(M)} is, as defined in [FO2], the Teichmüller space of negatively curved metrics on M. In particular we conclude that T sec < 0 (M){\mathcal{T}^{\,\,sec <0 }(M)} is, in general, not connected. Two remarks: (1) the nontrivial elements in pkMET sec < 0 (M){\pi_{k}\mathcal{MET}^{\,\,sec <0 }(M)} constructed in [FO3] have trivial image by the map induced by MET sec < 0 (M)?T sec < 0 (M){\mathcal{MET}^{\,\,sec <0 }(M)\rightarrow\mathcal{T}^{\,\,sec <0 }(M)} ; (2) the nonzero classes in pkT sec < 0 (M){\pi_{k}\mathcal{T}^{\,\,sec <0 }(M)} constructed in [FO2] are not in the image of the map induced by MET sec < 0 (M)?T sec < 0 (M){\mathcal{MET}^{\,\,sec <0 }(M)\rightarrow\mathcal{T}^{\,\,sec <0 }(M)} ; the nontrivial classes in pkT sec < 0 (M){\pi_{k}\mathcal{T}^{\,\,sec <0 }(M)} given here, besides coming from MET sec < 0 (M){\mathcal{MET}^{\,\,sec <0 }(M)} and being harder to construct, have a different nature and genesis: the former classes – given in [FO2] – come from the existence
of exotic spheres, while the latter classes – given here – arise from the non-triviality and structure of certain homotopy
groups of the space of pseudo-isotopies of the circle
\mathbbS1{\mathbb{S}^1}. The strength of the new techniques used here allowed us to prove also a homology version of Theorem A, which is given in
Theorem B. 相似文献
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15.
Heping Zhang 《Order》2010,27(2):101-113
Let G be a plane bipartite graph and M(G){\cal M}(G) the set of perfect matchings of G. A property that the Z-transformation digraph of perfect matchings of G is acyclic implies a partially ordered relation on M(G){\cal M}(G). It was shown that M(G){\cal M}(G) is a distributive lattice if G is (weakly) elementary. Based on the unit decomposition of alternating cycle systems, in this article we show that the poset
M(G){\cal M}(G) is direct sum of finite distributive lattices if G is non-weakly elementary; Further, if G is elementary, then the height of distributive lattice M(G){\cal M}(G) equals the diameter of Z-transformation graph, and both quantities have a sharp upper bound
é\fracn(n+2)4ù\lceil\frac{n(n+2)}{4}\rceil, where n denotes the number of inner faces of G. 相似文献
16.
Let G be a group and π
e
(G) be the set of element orders of G. Let k ? pe(G){k\in\pi_e(G)} and m
k
be the number of elements of order k in G. Let nse(G) = {mk|k ? pe(G)}{{\rm nse}(G) = \{m_k|k\in\pi_e(G)\}} . In Shen et al. (Monatsh Math, 2009), the authors proved that A4 @ PSL(2, 3), A5 @ PSL(2, 4) @ PSL(2,5){A_4\cong {\rm PSL}(2, 3), A_5\cong \rm{PSL}(2, 4)\cong \rm{PSL}(2,5)} and A6 @ PSL(2,9){A_6\cong \rm{PSL}(2,9)} are uniquely determined by nse(G). In this paper, we prove that if G is a group such that nse(G) = nse(PSL(2, q)), where q ? {7,8,11,13}{q\in\{7,8,11,13\}} , then G @ PSL(2,q){G\cong {PSL}(2,q)} . 相似文献
17.
Mohammad Zarrin 《Archiv der Mathematik》2011,96(3):225-226
For any group G, let C(G){\mathcal{C}(G)} denote the set of centralizers of G. We say that a group G has n centralizers (G is a Cn{\mathcal{C}_n}-group) if |C(G)| = n{|\mathcal{C}(G)| = n}. In this note, we show that the derived length of a soluble Cn{\mathcal{C}_n}-group (not necessarily finite) is bounded by a function of n. 相似文献
18.
Let G = (V, E) be an undirected graph and C(G){{\mathcal C}(G)} denote the set of all cycles in G. We introduce a graph invariant cycle discrepancy, which we define as
${\rm cycdisc}(G) = \min_{\chi: V \mapsto \{+1, -1\}}
\max_{ C \in {\mathcal C} (G)}
\left|\sum_{v \in C}
\chi(v)\right|.${\rm cycdisc}(G) = \min_{\chi: V \mapsto \{+1, -1\}}
\max_{ C \in {\mathcal C} (G)}
\left|\sum_{v \in C}
\chi(v)\right|. 相似文献
19.
Let G = exp ${\mathfrak{g}}$ be a connected, simply connected, nilpotent Lie group and let ω be a continuous symmetric weight on G with polynomial growth. In the weighted group algebra ${L^{1}_{\omega}(G)}$ we determine the minimal ideal of given hull ${\{\pi_{l'} \in \hat{G} | l' \in l + \mathfrak{n}^{\perp}\}}$ , where ${\mathfrak{n}}$ is an ideal contained in ${\mathfrak{g}(l)}$ , and we characterize all the L ∞(G/N)-invariant ideals (where ${N = {\rm exp}\, \mathfrak{n}}$ ) of the same hull. They are parameterized by a set of G-invariant, translation invariant spaces of complex polynomials on N dominated by ω and are realized as kernels of specially built induced representations. The result is particularly simple if the co-adjoint orbit of l is flat. 相似文献
20.
An edge coloring is called vertex-distinguishing if every two distinct vertices are incident to different sets of colored edges. The minimum number of colors required for
a vertex-distinguishing proper edge coloring of a simple graph G is denoted by c¢vd(G){\chi'_{vd}(G)}. It is proved that c¢vd(G) £ D(G)+5{\chi'_{vd}(G)\leq\Delta(G)+5} if G is a connected graph of order n ≥ 3 and
s2(G) 3 \frac2n3{\sigma_{2}(G)\geq\frac{2n}{3}}, where σ
2(G) denotes the minimum degree sum of two nonadjacent vertices in G. 相似文献
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