共查询到20条相似文献,搜索用时 46 毫秒
1.
Ricerche di Matematica - Let $${\mathfrak {X}}$$ be a class of simple groups with a completeness property $$\pi ({\mathfrak {X}}) = \mathrm {char} \, {\mathfrak {X}}$$ . A formation is a class of... 相似文献
2.
This paper deals with the splitting number ${\mathfrak{s}}$ and polarized partition relations. In the first section we define the notion of strong splitting families, and prove that its existence is equivalent to the failure of the polarized relation $$\left(\begin{array}{lll}\mathfrak{s} \\ \omega \end{array} \right) \rightarrow {\left(\begin{array}{ll}\mathfrak{s} \\ \omega \end{array} \right)}^{1, 1}_{2}$$ . We show that the existence of a strong splitting family is consistent with ZFC, and that the strong splitting number equals the splitting number, when it exists. Consequently, we can put some restriction on the possibility that s is singular. In the second section we deal with the polarized relation under the weak diamond, and we prove that the strong polarized relation $$\left(\begin{array}{lll}2^{\omega} \\ \omega \end{array} \right) \rightarrow {\left(\begin{array}{ll}2^{\omega} \\ \omega \end{array} \right)}^{1, 1}_{2}$$ is consistent with ZFC, even when cf ${(2^{\omega}) = \aleph_{1}}$ (hence the weak diamond holds). 相似文献
3.
A. I. Molev 《Selecta Mathematica, New Series》2006,12(1):1-38
Analogs of the classical Sylvester theorem have been known for matrices with entries in noncommutative algebras including
the quantized algebra of functions on GL
N
and the Yangian for
$$ \mathfrak{g}\mathfrak{l}_{{N}} $$ . We prove a version of this theorem for the twisted Yangians
$$ {\text{Y(}}\mathfrak{g}_{N} {\text{)}} $$associated with the orthogonal and symplectic Lie algebras
$$ \mathfrak{g}_{N} = \mathfrak{o}_{N} {\text{ or }}\mathfrak{s}\mathfrak{p}_{N} $$. This gives rise to representations of
the twisted Yangian
$$ {\text{Y}}{\left( {\mathfrak{g}_{{N - M}} } \right)} $$ on the space of homomorphisms
$$ {\text{Hom}}_{{\mathfrak{g}_{M} }} {\left( {W,V} \right)} $$, where W and V are finite-dimensional irreducible modules over
$$ \mathfrak{g}_{{M}} {\text{ and }}\mathfrak{g}_{{N}} $$, respectively. In the symplectic case these representations turn
out to be irreducible and we identify them by calculating the corresponding Drinfeld polynomials.We also apply the quantum
Sylvester theorem to realize the twisted Yangian as a projective limit of certain centralizers in universal enveloping algebras. 相似文献
4.
A. I. Molev 《Selecta Mathematica, New Series》2005,12(1):1-38
Analogs of the classical Sylvester theorem have been known for matrices with entries in noncommutative algebras including
the quantized algebra of functions on GLN and the Yangian for
$$ \mathfrak{g}\mathfrak{l}_{{N}} $$ . We prove a version of this theorem for the twisted Yangians
$$ {\text{Y(}}\mathfrak{g}_{N} {\text{)}} $$associated with the orthogonal and symplectic Lie algebras
$$ \mathfrak{g}_{N} = \mathfrak{o}_{N} {\text{ or }}\mathfrak{s}\mathfrak{p}_{N} $$. This gives rise to representations of
the twisted Yangian
$$ {\text{Y}}{\left( {\mathfrak{g}_{{N - M}} } \right)} $$ on the space of homomorphisms
$$ {\text{Hom}}_{{\mathfrak{g}_{M} }} {\left( {W,V} \right)} $$, where W and V are finite-dimensional irreducible modules over
$$ \mathfrak{g}_{{M}} {\text{ and }}\mathfrak{g}_{{N}} $$, respectively. In the symplectic case these representations turn
out to be irreducible and we identify them by calculating the corresponding Drinfeld polynomials.We also apply the quantum
Sylvester theorem to realize the twisted Yangian as a projective limit of certain centralizers in universal enveloping algebras. 相似文献
5.
Shahram Rezaei 《Archiv der Mathematik》2018,110(6):563-572
Let R be a commutative Noetherian ring, \({\mathfrak {a}}\) an ideal of R, M a finitely generated R-module, and \({\mathcal {S}}\) a Serre subcategory of the category of R-modules. We introduce the concept of \({\mathcal {S}}\)-minimax R-modules and the notion of the \({\mathcal {S}}\)-finiteness dimension and we will prove that: (i) If \({\text {H}}_{\mathfrak {a}}^{0}(M), \cdots ,{\text {H}}_{\mathfrak {a}}^{n-1}(M)\) are \({\mathcal {S}}\)-minimax, then the set \(\lbrace \mathfrak {p}\in {\text {Ass}}_R( {\text {H}}_{\mathfrak {a}}^{n}(M)) \vert R/\mathfrak {p}\notin {\mathcal {S}}\rbrace \) is finite. This generalizes the main results of Brodmann–Lashgari (Proc Am Math Soc 128(10):2851–2853, 2000), Quy (Proc Am Math Soc 138:1965–1968, 2010), Bahmanpour–Naghipour (Proc Math Soc 136:2359–2363, 2008), Asadollahi–Naghipour (Commun Algebra 43:953–958, 2015), and Mehrvarz et al. (Commun Algebra 43:4860–4872, 2015). (ii) If \({\mathcal {S}}\) satisfies the condition \(C_{\mathfrak {a}}\), then This is a formulation of Faltings’ Local-global principle for the \({\mathcal {S}}\)-minimax local cohomology modules. (iii) \( \sup \lbrace i\in {\mathbb {N}}_{0} \vert {\text {H}}_{\mathfrak {a}}^{i}(M) \text { is not } {\mathcal {S}}\text {-minimax} \rbrace = \sup \lbrace i\in {\mathbb {N}}_{0} \vert {\text {H}}_{\mathfrak {a}}^{i}(M) \text { is not in } {\mathcal {S}} \rbrace \).
相似文献
$$\begin{aligned} f_{\mathfrak {a}}^{{\mathcal {S}}}(M):=\inf \lbrace f_{\mathfrak {a}R_{\mathfrak {p}}}(M_{\mathfrak {p}}) \vert \mathfrak {p}\in {\text {Supp}}_R(M/ \mathfrak {a}M) \text { and } R/\mathfrak {p}\notin {\mathcal {S}} \rbrace \end{aligned}$$
$$\begin{aligned} f_{\mathfrak {a}}^{{\mathcal {S}}}(M)= \inf \lbrace i\in {\mathbb {N}}_{0} \vert {\text {H}}_{\mathfrak {a}}^{i}(M) \text { is not } {\mathcal {S}}\hbox {-}minimax\rbrace . \end{aligned}$$
6.
Theoretical and Mathematical Physics - The problem of providing complete presentations of reduction algebras associated to a pair of Lie algebras $$( \mathfrak{G} , \mathfrak{g} )$$ has previously... 相似文献
7.
V. Yu. Popov 《Algebra and Logic》2001,40(1):55-66
It is proved that there exists an infinite sequence of finitely based semigroup varieties
such that, for all i, an equational theory for
and for the class
of all finite semigroups in
is undecidable while an equational theory for
and for the class
of all finite semigroups in
is decidable. An infinite sequence of finitely based semigroup varieties
is constructed so that, for all i, an equational theory for
and for the class
of all finite semigroups in
is decidable whicle an equational theory for
and for the class
of all finite semigroups in
is not. 相似文献
8.
А. А. Привалов 《Analysis Mathematica》1987,13(2):139-152
В статье даны полные д оказательства следу ющих утверждений. Пустьω — непрерывная неубывающая полуадд итивная функций на [0, ∞),ω(0)=0 и пусть M?[0, 1] — матрица узл ов интерполирования. Если $$\mathop {\lim sup}\limits_{n \to \infty } \omega \left( {\frac{1}{n}} \right)\log n > 0$$ то существует точкаx 0∈[0,1] и функцияf ∈ С[0,1] таки е, чтоω(f, δ)=О(ω(δ)), для которой $$\mathop {\lim sup}\limits_{n \to \infty } |L_n (\mathfrak{M},f,x_0 ) - f(x_0 )| > 0$$ Если же $$\mathop {\lim sup}\limits_{n \to \infty } \omega \left( {\frac{1}{n}} \right)\log n = \infty$$ , то существуют множес твоE второй категори и и функцияf ∈ С[0,1],ω(f, δ)=o(ω(δ)) та кие, что для всехx∈E $$\mathop {\lim sup}\limits_{n \to \infty } |L_n (\mathfrak{M},f,x)| = \infty$$ . Исправлена погрешно сть, допущенная автор ом в [5], и отмеченная в работе П. Вертеши [9]. 相似文献
9.
A complete Boolean algebra
\mathbbB{\mathbb{B}}satisfies property ((h/2p)){(\hbar)}iff each sequence x in
\mathbbB{\mathbb{B}}has a subsequence y such that the equality lim sup z
n
= lim sup y
n
holds for each subsequence z of y. This property, providing an explicit definition of the a posteriori convergence in complete Boolean algebras with the sequential
topology and a characterization of sequential compactness of such spaces, is closely related to the cellularity of Boolean
algebras. Here we determine the position of property ((h/2p)){(\hbar)}with respect to the hierarchy of conditions of the form κ-cc. So, answering a question from Kurilić and Pavlović (Ann Pure Appl Logic 148(1–3):49–62, 2007), we show that ${``\mathfrak{h}{\rm -cc}\Rightarrow (\hbar)"}${``\mathfrak{h}{\rm -cc}\Rightarrow (\hbar)"}is not a theorem of ZFC and that there is no cardinal
\mathfrakk{\mathfrak{k}}, definable in ZFC, such that ${``\mathfrak{k} {\rm -cc} \Leftrightarrow (\hbar)"}${``\mathfrak{k} {\rm -cc} \Leftrightarrow (\hbar)"}is a theorem of ZFC. Also, we show that the set { k: each k-cc c.B.a. has ((h/2p) ) }{\{ \kappa : {\rm each}\, \kappa{\rm -cc\, c.B.a.\, has}\, (\hbar ) \}}is equal to
[0, \mathfrakh){[0, \mathfrak{h})}or
[0, \mathfrak h]{[0, {\mathfrak h}]}and that both values are consistent, which, with the known equality
{k: each c.B.a. having ((h/2p) ) has the k-cc } = [\mathfrak s, ¥){{\{\kappa : {\rm each\, c.B.a.\, having }\, (\hbar )\, {\rm has\, the}\, \kappa {\rm -cc } \} =[{\mathfrak s}, \infty )}}completes the picture. 相似文献
10.
Lutz Strüngmann 《Archiv der Mathematik》2006,86(3):193-204
Let R be a unital associative ring and
two classes of left R-modules. In this paper we introduce the notion of a
In analogy to classical cotorsion pairs as defined by Salce [10], a pair
of subclasses
and
is called a
if it is maximal with respect to the classes
and the condition
for all
and
Basic properties of
are stated and several examples in the category of abelian groups are studied.
Received: 17 March 2005 相似文献
11.
Let(M,ω)be a symplectic manifold.In this paper,the authors consider the notions of musical(bemolle and diesis)isomorphisms ω~b:T M→T~*M and ω~?:T~*M→TM between tangent and cotangent bundles.The authors prove that the complete lifts of symplectic vector field to tangent and cotangent bundles is ω~b-related.As consequence of analyze of connections between the complete lift ~cω_(T M )of symplectic 2-form ω to tangent bundle and the natural symplectic 2-form dp on cotangent bundle,the authors proved that dp is a pullback o f~cω_(TM)by ω~?.Also,the authors investigate the complete lift ~cφ_T~*_M )of almost complex structure φ to cotangent bundle and prove that it is a transform by ω~?of complete lift~cφ_(T M )to tangent bundle if the triple(M,ω,φ)is an almost holomorphic A-manifold.The transform of complete lifts of vector-valued 2-form is also studied. 相似文献
12.
Complementing the results of (Lotta and Nacinovich, Adv. Math. 191(1): 114–146, 2005), we show that the minimal orbit M of a real form G of a semisimple complex Lie group in a flag manifold is CR-symmetric (see (Kaup and Zaitsev Adv. Math. 149(2):145–181, 2000)) if and only if the corresponding CR algebra admits a gradation compatible with the CR structure.
相似文献
13.
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
14.
I. V. Sokolenko 《Ukrainian Mathematical Journal》2004,56(5):799-816
We obtain asymptotic formulas for the deviations of Fourier operators on the classes of continuous functions
and
in the uniform metric. We also establish asymptotic laws of decrease of functionals characterizing the problem of the simultaneous approximation of
-integrals of continuous functions by Fourier operators in the uniform metric.Translated from Ukrainskyi Matematychnyi Zhurnal, Vol. 56, No. 5, pp. 663–676, May, 2004. 相似文献
15.
Let E be a non empty set, let P : = E × E,
:= {x × E|x ∈ E},
:= {E × x|x ∈ E}, and
:= {C ∈ 2
P
|∀X ∈
: |C ∩ X| = 1} and let
. Then the quadruple
resp.
is called chain structure resp. maximal chain structure. We consider the maximal chain structure
as an envelope of the chain structure
. Particular chain structures are webs, 2-structures, (coordinatized) affine planes, hyperbola structures or Minkowski planes.
Here we study in detail the groups of automorphisms
,
,
,
related to a maximal chain structure
. The set
of all chains can be turned in a group
such that the subgroup
of
generated by
the left-, by
the right-translations and by ι the inverse map of
is isomorphic to
(cf. (2.14)). 相似文献
16.
Andrew Raich 《Mathematische Zeitschrift》2007,256(1):193-220
Let be a subharmonic, nonharmonic polynomial and a parameter. Define , a closed, densely defined operator on . If and , we solve the heat equations , u(0,z) = f(z) and , . We write the solutions via heat semigroups and show that the solutions can be written as integrals against distributional
kernels. We prove that the kernels are C
∞ off of the diagonal {(s, z, w) : s = 0 and z = w} and find pointwise bounds for the kernels and their derivatives.
相似文献
17.
Sara C. Billey William Jockusch Richard P. Stanley 《Journal of Algebraic Combinatorics》1993,2(4):345-374
Schubert polynomials were introduced by Bernstein et al. and Demazure, and were extensively developed by Lascoux, Schützenberger, Macdonald, and others. We give an explicit combinatorial interpretation of the Schubert polynomial
in terms of the reduced decompositions of the permutation w. Using this result, a variation of Schensted's correspondence due to Edelman and Greene allows one to associate in a natural way a certain set
of tableaux with w, each tableau contributing a single term to
. This correspondence leads to many problems and conjectures, whose interrelation is investigated. In Section 2 we consider permutations with no decreasing subsequence of length three (or 321-avoiding permutations). We show for such permutations that
is a flag skew Schur function. In Section 3 we use this result to obtain some interesting properties of the rational function
, where
denotes a skew Schur function.Sara C. Billey: Supported by the National Physical Science Consortium. William Jockusch: Supported by an NSF Graduate Fellowship. Richard P. Stanley: Partially supported by NSF grants DMS-8901834 and DMS-9206374 相似文献
18.
De Falco Maria de Giovanni Francesco Musella Carmela 《Monatshefte für Mathematik》2020,191(2):249-256
Monatshefte für Mathematik - If G is an uncountable group of regular cardinality $$\aleph $$, we shall denote by $${\mathfrak {L}L}_\aleph (G)$$ the set of all subgroups of G of cardinality... 相似文献
19.
Theoretical and Mathematical Physics - We consider a realization of representations of the Lie algebra $$\mathfrak{o}_5$$ in the space of functions on the group $$Spin_5\simeq Sp_4$$ . In the... 相似文献
20.
In this paper, we introduce one-parameter homothetic motions in the generalized complex number plane (\({\mathfrak{p}}\)-complex plane)wheresuch that \({-\infty < \mathfrak{p} < \infty}\). The velocities, accelerations and pole points of the motion are analysed. Moreover, three generalized complex number planes, of which two are moving and the other one is fixed, are considered and a canonical relative system for one-parameter planar homothetic motion in \({\mathbb{C}_{J}}\) is defined. Euler-Savary formula, which gives the relationship between the curvatures of trajectory curves, during the one-parameter homothetic motions, is obtained with the aim of this canonical relative system.
相似文献
$$\mathbb{C}_{J}=\left\{x+Jy:\,\,\, x,y \in \mathbb{R},\quad J^2=\mathfrak{p},\quad \mathfrak{p} \in \{-1,0,1\} \right\} \subset \mathbb{C}_\mathfrak{p}$$
$$\mathbb{C}_\mathfrak{p}=\{x+Jy:\,\,\, x,y \in \mathbb{R}, \quad J^2=\mathfrak{p}\}$$