共查询到20条相似文献,搜索用时 421 毫秒
1.
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
2.
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
3.
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
4.
5.
Journal of Algebraic Combinatorics - By viewing $$\tilde{A}$$ and $$\tilde{D}$$ type cluster algebras as triangulated surfaces, we find all cluster variables in terms of either (i) the frieze... 相似文献
6.
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
$$\mathbb{C}_{J}=\left\{x+Jy:\,\,\, x,y \in \mathbb{R},\quad J^2=\mathfrak{p},\quad \mathfrak{p} \in \{-1,0,1\} \right\} \subset \mathbb{C}_\mathfrak{p}$$
$$\mathbb{C}_\mathfrak{p}=\{x+Jy:\,\,\, x,y \in \mathbb{R}, \quad J^2=\mathfrak{p}\}$$
7.
David Eelbode 《Advances in Applied Clifford Algebras》2007,17(4):635-649
We introduce a framework for studying differential operators which are invariant with respect to the real (complex) symplectic
Lie algebra
(
), associated to a quaternionic structure on a vector space
. To do so, these algebras are realized within the orthogonal Lie algebra
. This leads in a natural way to a refinement of the recently introduced notion of complex Hermitean Clifford analysis, in
which four variations of the classical Dirac operator play a dominant role.
David Eelbode: Postdoctoral fellow supported by the F.W.O. Vlaanderen (Belgium). 相似文献
8.
Theoretical and Mathematical Physics - We study the class of $$ \mathfrak{o} _{2n+1}$$ -invariant quantum integrable models in the framework of the algebraic Bethe ansatz and propose a construction... 相似文献
9.
Let E?R be an interval. By studying an admissible family of branching mechanisms{ψt,t ∈E} introduced in Li [Ann. Probab., 42, 41-79(2014)], we construct a decreasing Levy-CRT-valued process {Tt, t ∈ E} by pruning Lévy trees accordingly such that for each t ∈E, Tt is a ψt-Lévy tree. We also obtain an analogous process {Tt*,t ∈E} by pruning a critical Levy tree conditioned to be infinite. Under a regular condition on the admissible family of branching mechanisms, we show that the law of {Tt,t ∈E} at the ascension time A := inf{t ∈E;Tt is finite} can be represented by{Tt*,t∈E}.The results generalize those studied in Abraham and Delmas [Ann. Probab., 40, 1167-1211(2012)]. 相似文献
10.
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
11.
Mathematical Notes - In the paper, the notion of an $$\mathfrak F^{\omega}$$ -abnormal (and $$\mathfrak F^{\omega}$$ -normal) maximal subgroup of a finite group is introduced, where $$\mathfrak F$$... 相似文献
12.
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
13.
Mathematical Notes - Let $$\mathfrak{F}$$ be a formation. Properties of the class $$\mathrm{w}^{*}\mathfrak{F}$$ of all groups $$G$$ for which $$\pi(G)\subseteq\pi(\mathfrak{F})$$ and the... 相似文献
14.
Theoretical and Mathematical Physics - We consider a realization of a representation of the $$ \mathfrak{sp} _4$$ Lie algebra in the space of functions on a Lie group $$Sp_4$$ . We find a function... 相似文献
15.
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
$$\begin{aligned} f_{\mathfrak {a}}^{{\mathcal {S}}}(M):=\inf \lbrace f_{\mathfrak {a}R_{\mathfrak {p}}}(M_{\mathfrak {p}}) \vert \mathfrak {p}\in {\text {Supp}}_R(M/ \mathfrak {a}M) \text { and } R/\mathfrak {p}\notin {\mathcal {S}} \rbrace \end{aligned}$$
$$\begin{aligned} f_{\mathfrak {a}}^{{\mathcal {S}}}(M)= \inf \lbrace i\in {\mathbb {N}}_{0} \vert {\text {H}}_{\mathfrak {a}}^{i}(M) \text { is not } {\mathcal {S}}\hbox {-}minimax\rbrace . \end{aligned}$$
16.
Mathematical Notes - A formation $$\mathfrak{F}$$ of finite groups is said to be superradical if it satisfies the following requirements: $$\bullet$$ $$\mathfrak{F}$$ is a normally hereditary... 相似文献
17.
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
18.
A. A. Dosiev 《Functional Analysis and Its Applications》2003,37(1):61-64
This note deals with homological characteristics of algebras of holomorphic functions of noncommuting variables generated by a finite-dimensional nilpotent Lie algebra
. It is proved that the embedding
of the universal enveloping algebra
of
into its Arens–Michael hull
is an absolute localization in the sense of Taylor provided that
相似文献
19.
Adamović Dražen Kac Victor G. Frajria Pierluigi Möseneder Papi Paolo Perše Ozren 《Selecta Mathematica, New Series》2018,24(3):2455-2498
Selecta Mathematica - We complete the classification of conformal embeddings of a maximally reductive subalgebra $$\mathfrak {k}$$ into a simple Lie algebra $$\mathfrak {g}$$ at non-integrable... 相似文献
20.
Ján Jakubík 《Czechoslovak Mathematical Journal》2008,58(3):833-848
Let be an infinite cardinal. We denote by the collection of all -representable Boolean algebras. Further, let be the collection of all generalized Boolean algebras B such that for each b ∈ B, the interval [0, b] of B belongs to . In this paper we prove that is a radical class of generalized Boolean algebras. Further, we investigate some related questions concerning lattice ordered
groups and generalized MV-algebras.
This work was supported by Science and Technology Assistance Agency under the contract No. APVT-51-032002.
This work has been partially supported by the Slovak Academy of Sciences via the project Center of Excellence-Physics of Information. 相似文献