共查询到20条相似文献,搜索用时 62 毫秒
1.
2.
Alexander Premet 《Inventiones Mathematicae》2010,181(2):395-420
Let ${\mathfrak{g}}Let
\mathfrakg{\mathfrak{g}} be a finite dimensional simple Lie algebra over an algebraically closed field
\mathbbK\mathbb{K} of characteristic 0. Let
\mathfrakg\mathbbZ{\mathfrak{g}}_{{\mathbb{Z}}} be a Chevalley ℤ-form of
\mathfrakg{\mathfrak{g}} and
\mathfrakg\Bbbk=\mathfrakg\mathbbZ?\mathbbZ\Bbbk{\mathfrak{g}}_{\Bbbk}={\mathfrak{g}}_{{\mathbb{Z}}}\otimes _{{\mathbb{Z}}}\Bbbk, where
\Bbbk\Bbbk is the algebraic closure of
\mathbbFp{\mathbb{F}}_{p}. Let
G\BbbkG_{\Bbbk} be a simple, simply connected algebraic
\Bbbk\Bbbk-group with
\operatornameLie(G\Bbbk)=\mathfrakg\Bbbk\operatorname{Lie}(G_{\Bbbk})={\mathfrak{g}}_{\Bbbk}. In this paper, we apply recent results of Rudolf Tange on the fraction field of the centre of the universal enveloping algebra
U(\mathfrakg\Bbbk)U({\mathfrak{g}}_{\Bbbk}) to show that if the Gelfand–Kirillov conjecture (from 1966) holds for
\mathfrakg{\mathfrak{g}}, then for all p≫0 the field of rational functions
\Bbbk (\mathfrakg\Bbbk)\Bbbk ({\mathfrak{g}}_{\Bbbk}) is purely transcendental over its subfield
\Bbbk(\mathfrakg\Bbbk)G\Bbbk\Bbbk({\mathfrak{g}}_{\Bbbk})^{G_{\Bbbk}}. Very recently, it was proved by Colliot-Thélène, Kunyavskiĭ, Popov, and Reichstein that the field of rational functions
\mathbbK(\mathfrakg){\mathbb{K}}({\mathfrak{g}}) is not purely transcendental over its subfield
\mathbbK(\mathfrakg)\mathfrakg{\mathbb{K}}({\mathfrak{g}})^{\mathfrak{g}} if
\mathfrakg{\mathfrak{g}} is of type B
n
, n≥3, D
n
, n≥4, E6, E7, E8 or F4. We prove a modular version of this result (valid for p≫0) and use it to show that, in characteristic 0, the Gelfand–Kirillov conjecture fails for the simple Lie algebras of the
above types. In other words, if
\mathfrakg{\mathfrak{g}} is of type B
n
, n≥3, D
n
, n≥4, E6, E7, E8 or F4, then the Lie field of
\mathfrakg{\mathfrak{g}} is more complicated than expected. 相似文献
3.
Christopher Kennedy 《Algebras and Representation Theory》2011,14(6):1187-1202
This paper continues the study of associative and Lie deep matrix algebras,
DM(X,\mathbbK){\mathcal{DM}}(X,{\mathbb{K}}) and
\mathfrakgld(X,\mathbbK){\mathfrak{gld}}(X,{\mathbb{K}}), and their subalgebras. After a brief overview of the general construction, balanced deep matrix subalgebras,
BDM(X,\mathbbK){\mathcal{BDM}}(X,{\mathbb{K}}) and
\mathfrakbld(X,\mathbbK){\mathfrak{bld}}(X,{\mathbb{K}}), are defined and studied for an infinite set X. The global structures of these two algebras are studied, devising a depth grading on both as well as determining their ideal
lattices. In particular,
\mathfrakbld(X,\mathbbK){\mathfrak{bld}}(X,{\mathbb{K}}) is shown to be semisimple. The Lie algebra
\mathfrakbld(X,\mathbbK){\mathfrak{bld}}(X,{\mathbb{K}}) possesses a deep Cartan decomposition and is locally finite with every finite subalgebra naturally enveloped by a semi-direct
product of
\mathfraksln{\mathfrak{{sl}_n}}’s. We classify all associative bilinear forms on
\mathfraksl2\mathfrakd{\mathfrak{sl}_2\mathfrak{d}} (a natural depth analogue of
\mathfraksl2{\mathfrak{{sl}_2}}) and
\mathfrakbld{\mathfrak{bld}}. 相似文献
4.
Helmut Zöschinger 《Archiv der Mathematik》2010,95(3):225-231
Let
(R,\mathfrak m){(R,\mathfrak m)} be a noetherian, local ring with completion [^(R)]{\hat{R}} . We show that R ì [^(R)]{R \subset \hat{R}} satisfies the condition Going up if and only if there exists to every artinian R-module M with
AnnR(M) ì \mathfrakp{{\rm Ann}_R(M) \subset \mathfrak{p}} a submodule U ì M{U \subset M} with
AnnR(U)=\mathfrakp.{{\rm {Ann}}_R(U)=\mathfrak{p}.} This is further equivalent to R being formal catenary, to α(R) = 0 and to
Hd\mathfrakq/\mathfrakp(R/\mathfrakp)=0{H^d_{\mathfrak{q}/\mathfrak{p}}(R/\mathfrak{p})=0} for all prime ideals
\mathfrakp ì \mathfrakq \subsetneq \mathfrakm{\mathfrak{p} \subset \mathfrak{q} \subsetneq \mathfrak{m}} where
d = dim(R/\mathfrakp){d = {\rm {dim}}(R/\mathfrak{p})}. 相似文献
5.
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
6.
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
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.
9.
Let
\mathfrakX{\mathfrak{X}} be a class of groups. A group G is called a minimal non-
\mathfrakX{\mathfrak{X}}-group if it is not an
\mathfrakX{\mathfrak{X}}-group but all of whose proper subgroups are
\mathfrakX{\mathfrak{X}}-groups. In [16], Xu proved that if G is a soluble minimal non-Baer-group, then G/G
′′ is a minimal non-nilpotent-group which possesses a maximal subgroup. In the present note, we prove that if G is a soluble minimal non-(finite-by-Baer)-group, then for all integer n ≥ 2, G/γ
n
(G′) is a minimal non-(finite-by-abelian)-group. 相似文献
10.
Let ${\mathbb {F}}
11.
Esteban Andruchow Jorge Antezana Gustavo Corach 《Integral Equations and Operator Theory》2010,67(4):451-466
Given a closed subspace ${\mathcal{S}}
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