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1.
In this paper we develop an abstract setup for hamiltonian group actions as follows: Starting with a continuous 2-cochain ω on a Lie algebra ${\mathfrak h}$ with values in an ${\mathfrak h}$ -module V, we associate subalgebras ${\mathfrak {sp}(\mathfrak h,\omega) \supseteq \mathfrak {ham}(\mathfrak h,\omega)}$ of symplectic, resp., hamiltonian elements. Then ${\mathfrak {ham}(\mathfrak h,\omega)}$ has a natural central extension which in turn is contained in a larger abelian extension of ${\mathfrak {sp}(\mathfrak h,\omega)}$ . In this setting, we study linear actions of a Lie group G on V which are compatible with a homomorphism ${\mathfrak g \to \mathfrak {ham}(\mathfrak h,\omega)}$ , i.e., abstract hamiltonian actions, corresponding central and abelian extensions of G and momentum maps ${J : \mathfrak g \to V}$ . 相似文献
2.
Victor Pambuccian 《Archiv der Mathematik》2010,95(3):293-300
It is shown that a mapping ${\varphi: \mathfrak{A}\rightarrow \mathfrak{B}}It is shown that a mapping
j: \mathfrakA? \mathfrakB{\varphi: \mathfrak{A}\rightarrow \mathfrak{B}} between models
\mathfrakA{\mathfrak{A}} and
\mathfrakB{\mathfrak{B}} of elementary plane hyperbolic geometry, coordinatized by Euclidean ordered fields, that maps triangles having the same area
and sharing a side into triangles that have the same property, must be a hyperbolic motion onto
j(\mathfrakA){\varphi(\mathfrak{A})}. The relations that Tarski and Szmielew used as primitives for geometry, the equidistance relation ≡ and the betweenness
relation B are shown to be positively existentially definable in terms of the quaternary relation Δ, with Δ(abcd) standing for “the triangles abc and abd have the same area.” 相似文献
3.
Violeta Petkova 《Archiv der Mathematik》2009,93(4):357-368
We study the spectrum σ(M) of the multipliers M which commute with the translations on weighted spaces ${L_{\omega}^{2}(\mathbb{R})}We study the spectrum σ(M) of the multipliers M which commute with the translations on weighted spaces
Lw2(\mathbbR){L_{\omega}^{2}(\mathbb{R})} For operators M in the algebra generated by the convolutions with
f ? Cc(\mathbb R){\phi \in {C_c(\mathbb {R})}} we show that [`(m(W))] = s(M){\overline{\mu(\Omega)} = \sigma(M)}, where the set Ω is determined by the spectrum of the shift S and μ is the symbol of M. For the general multipliers M we establish that [`(m(W))]{\overline{\mu(\Omega)}} is included in σ(M). A generalization of these results is given for the weighted spaces
L2w(\mathbb Rk){L^2_{\omega}(\mathbb {R}^{k})} where the weight ω has a special form. 相似文献
4.
Hiroaki Minami 《Archive for Mathematical Logic》2010,49(4):501-518
We investigate splitting number and reaping number for the structure (ω)
ω
of infinite partitions of ω. We prove that
\mathfrakrd £ non(M),non(N),\mathfrakd{\mathfrak{r}_{d}\leq\mathsf{non}(\mathcal{M}),\mathsf{non}(\mathcal{N}),\mathfrak{d}} and
\mathfraksd 3 \mathfrakb{\mathfrak{s}_{d}\geq\mathfrak{b}} . We also show the consistency results ${\mathfrak{r}_{d} > \mathfrak{b}, \mathfrak{s}_{d} < \mathfrak{d}, \mathfrak{s}_{d} < \mathfrak{r}, \mathfrak{r}_{d} < \mathsf{add}(\mathcal{M})}${\mathfrak{r}_{d} > \mathfrak{b}, \mathfrak{s}_{d} < \mathfrak{d}, \mathfrak{s}_{d} < \mathfrak{r}, \mathfrak{r}_{d} < \mathsf{add}(\mathcal{M})} and ${\mathfrak{s}_{d} > \mathsf{cof}(\mathcal{M})}${\mathfrak{s}_{d} > \mathsf{cof}(\mathcal{M})} . To prove the consistency
\mathfrakrd < add(M){\mathfrak{r}_{d} < \mathsf{add}(\mathcal{M})} and
\mathfraksd < cof(M){\mathfrak{s}_{d} < \mathsf{cof}(\mathcal{M})} we introduce new cardinal invariants
\mathfrakrpair{\mathfrak{r}_{pair}} and
\mathfrakspair{\mathfrak{s}_{pair}} . We also study the relation between
\mathfrakrpair, \mathfrakspair{\mathfrak{r}_{pair}, \mathfrak{s}_{pair}} and other cardinal invariants. We show that
cov(M),cov(N) £ \mathfrakrpair £ \mathfraksd,\mathfrakr{\mathsf{cov}(\mathcal{M}),\mathsf{cov}(\mathcal{N})\leq\mathfrak{r}_{pair}\leq\mathfrak{s}_{d},\mathfrak{r}} and
\mathfraks £ \mathfrakspair £ non(M),non(N){\mathfrak{s}\leq\mathfrak{s}_{pair}\leq\mathsf{non}(\mathcal{M}),\mathsf{non}(\mathcal{N})} . 相似文献
5.
Milo? S. Kurili? 《Order》2012,29(1):119-129
A family P ì [w]w{\mathcal P} \subset [\omega]^\omega is called positive iff it is the union of some infinite upper set in the Boolean algebra P(ω)/Fin. For example, if I ì P(w){\mathcal I} \subset P(\omega) is an ideal containing the ideal Fin of finite subsets of ω, then P(w) \IP(\omega) \setminus {\mathcal I} is a positive family and the set
Dense(\mathbb Q)\mbox{Dense}({\mathbb Q}) of dense subsets of the rational line is a positive family which is not the complement of some ideal on
P(\mathbb Q)P({\mathbb Q}). We prove that, for a positive family P{\mathcal P}, the order types of maximal chains in the complete lattice áP è{?}, ì ?\langle {\mathcal P} \cup \{\emptyset\}, \subset \rangle are exactly the order types of compact nowhere dense subsets of the real line having the minimum non-isolated. Also we compare
this result with the corresponding results concerning maximal chains in the Boolean algebras P(ω) and
Intalg[0,1)\mathbb R\mbox{Intalg}[0,1)_{{\mathbb R}} and the poset
E(\mathbb Q)E({\mathbb Q}), where
E(\mathbb Q)E({\mathbb Q}) is the set of elementary submodels of the rational line. 相似文献
6.
Let ${\mathbb {F}}Let
\mathbb F{\mathbb {F}} a finite field. We show that the universal characteristic factor for the Gowers–Host–Kra uniformity seminorm U
k
(X) for an ergodic action
(Tg)g ? \mathbb Fw{(T_{g})_{{g} \in \mathbb {F}^{\omega}}} of the infinite abelian group
\mathbb Fw{\mathbb {F}^{\omega}} on a probability space X = (X, B, m){X = (X, \mathcal {B}, \mu)} is generated by phase polynomials f: X ? S1{\phi : X \to S^{1}} of degree less than C(k) on X, where C(k) depends only on k. In the case where
k £ char(\mathbb F){k \leq {\rm char}(\mathbb {F})} we obtain the sharp result C(k) = k. This is a finite field counterpart of an analogous result for
\mathbb Z{\mathbb {Z}} by Host and Kra [HK]. In a companion paper [TZ] to this paper, we shall combine this result with a correspondence principle
to establish the inverse theorem for the Gowers norm in finite fields in the high characteristic case
k £ char(\mathbb F){k \leq {\rm char}(\mathbb {F})} , with a partial result in low characteristic. 相似文献
7.
Anton S. Galaev 《Annals of Global Analysis and Geometry》2012,42(1):1-27
Possible irreducible holonomy algebras
\mathfrakg ì \mathfrakosp(p, q|2m){\mathfrak{g}\subset\mathfrak{osp}(p, q|2m)} of Riemannian supermanifolds under the assumption that
\mathfrakg{\mathfrak{g}} is a direct sum of simple Lie superalgebras of classical type and possibly of a 1-dimensional center are classified. This
generalizes the classical result of Marcel Berger about the classification of irreducible holonomy algebras of pseudo-Riemannian
manifolds. 相似文献
8.
Harald Woracek 《Monatshefte für Mathematik》2012,33(3):105-149
A string is a pair (L, \mathfrakm){(L, \mathfrak{m})} where L ? [0, ¥]{L \in[0, \infty]} and \mathfrakm{\mathfrak{m}} is a positive, possibly unbounded, Borel measure supported on [0, L]; we think of L as the length of the string and of \mathfrakm{\mathfrak{m}} as its mass density. To each string a differential operator acting in the space L2(\mathfrakm){L^2(\mathfrak{m})} is associated. Namely, the Kreĭn–Feller differential operator -D\mathfrakmDx{-D_{\mathfrak{m}}D_x} ; its eigenvalue equation can be written, e.g., as
f¢(x) + z ò0L f(y) d\mathfrakm(y) = 0, x ? \mathbb R, f¢(0-) = 0.f^{\prime}(x) + z \int_0^L f(y)\,d\mathfrak{m}(y) = 0,\quad x \in\mathbb R,\ f^{\prime}(0-) = 0. 相似文献
9.
Let ${s,\,\tau\in\mathbb{R}}
10.
Amol Sasane 《Complex Analysis and Operator Theory》2012,6(2):465-475
Let
\mathbb Dn:={z=(z1,?, zn) ? \mathbb Cn:|zj| < 1, j=1,?, n}{\mathbb {D}^n:=\{z=(z_1,\ldots, z_n)\in \mathbb {C}^n:|z_j| < 1, \;j=1,\ldots, n\}}, and let
[`(\mathbbD)]n{\overline{\mathbb{D}}^n} denote its closure in
\mathbb Cn{\mathbb {C}^n}. Consider the ring
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