共查询到20条相似文献,搜索用时 19 毫秒
1.
We extend the Capelli identity from the Lie algebra to the other classical Lie algebras and . We employ the theory of reductive dual pairs due to Howe. Received: 12 February 1997 / in revised form: 24 July 1998 相似文献
2.
3.
Lie algebras graded by finite irreducible reduced root systems have been classified up to central extensions by Berman and
Moody, Benkart and Zelmanov, and Neher. In this paper we determine the central extensions of these Lie algebras and hence
describe them completely up to isomorphism.
Received: 22 May 1997 / in final form: 13 January 1999 相似文献
4.
Julius Borcea 《Mathematische Zeitschrift》2001,237(2):301-319
Given an affine Kac-Moody Lie algebra of arbitrary type, we determine certain minimal sets of annihilating fields of standard -modules. We then use these sets in order to obtain a characterization of standard -modules in terms of irreducible loop -modules, which proves to be a useful tool for combinatorial constructions of bases for standard -modules.
Received April 21 , 1999; in final form September 8, 1999 / Published online February 5, 2001 相似文献
5.
Yun Gao 《manuscripta mathematica》1998,97(2):233-249
We construct degenerate extended affine Lie algebras from a given nondegenerate extended affine Lie algebra and show that
all degenerate extended affine Lie algebras are obtained in this way.
Received: 21 January 1997 相似文献
6.
Let B be a block of the group algebra KG of a finite Group G over an algebraically closed field K. We prove that every degeneration of finite dimensional B-modules is given by short exact sequences if and only if B is of finite representation type.
Received: 7 July 1997 相似文献
7.
Xiaoping Xu 《manuscripta mathematica》1999,100(4):489-518
In this paper, we introduce two new families of infinite-dimensional simple Lie algebras and a new family of infinite-dimensional
simple Lie superalgebras. These algebras can be viewed as generalizations of the Block algebras.
Received: 3 March 1999 相似文献
8.
Jon F. Carlson 《manuscripta mathematica》1998,97(3):303-307
Let P be a finite p-group, and let k a field of characteristic p>0. We prove that a finietly generated kG-module M is endotrivial if and only if
where PHom (-,-) is the set of endomorphisms which factor through projective modules.
Received: 23 January 1998 相似文献
9.
10.
We describe some algebraic models for equivariant rational and p-adic homotopy theory over Abelian compact Lie groups.
Received: 12 February 2001; in final form: 15 August 2001 / Published online: 28 February 2002 相似文献
11.
Helmut Völklein 《Mathematische Annalen》1998,311(3):421-438
12.
Supported by NSF grants DMS-9001689 and DMS-9301929 相似文献
13.
Gerhard Röhrle 《manuscripta mathematica》1999,98(1):9-20
For a linear algebraic group G over an algebraically closed field k and a parabolic subgroup P of G the modality of P is defined to be the maximal number of parameters upon which a family of G-orbits on Lie P
u
depends and it is denoted by mod P, where P
u
is the unipotent radical of P. The principal aim of this note is a generalization of two basic “monotonicity” results from [19] to positive characteristic:
(1) If Θ is a semisimple automorphism of G and P is Θ-stable, then mod P
\Θ≤ mod P. (2) If G is reductive, char k is a good prime for G, and H is a closed reductive subgroup of G normalized by a maximal torus T⊂P of G, then mod (P∩H)≤ mod P.
Received: 22 April 1998 / Revised version: 3 July 1998 相似文献
14.
We compute the inverse image of a functional in the Zassenhaus variety. We apply this computation to describe the category of representations for a regular functional. Received November 11, 1997; in final form February 9, 1998 相似文献
15.
Triangulated categories and Kac-Moody algebras 总被引:7,自引:0,他引:7
By using the Ringel-Hall algebra approach, we find a Lie algebra arising in each triangulated category with T 2=1, where T is the translation functor. In particular, the generic form of the Lie algebras determined by the root categories, the 2-period orbit categories of the derived categories of finite dimensional hereditary associative algebras, gives a realization of all symmetrizable Kac-Moody Lie algebras. Oblatum 4-XII-1998 & 11-XI-1999?Published online: 21 February 2000 相似文献
16.
Fabio Gavarini 《Mathematische Zeitschrift》2000,234(1):9-52
Let be an untwisted affine Kac-Moody algebra, with its Sklyanin-Drinfel'd structure of Lie bialgebra, and let be the dual Lie bialgebra. By dualizing the quantum double construction – via formal Hopf algebras – we construct a new quantum
group , dual of . Studying its specializations at roots of 1 (in particular, its semi-classical limits), we prove that it yields quantizations
of and (the formal Poisson group attached to ), and we construct new quantum Frobenius morphisms. The whole picture extends to the untwisted affine case the results known
for quantum groups of finite type.
Received January 27, 1999 相似文献
17.
Helge Glöckner 《manuscripta mathematica》1998,97(2):205-215
Let G be a p-adic Lie group. Then G is a locally compact, totally disconnected group, to which Willis [14] associates its scale function G : G→ℕ. We show that s can be computed on the Lie algebra level. The image of s consists of powers of p. If G is a linear algebraic group over ℚ
p
, s(x)=s(h) is determined by the semisimple part h of x∈G. For every finite extension K of ℚ
p
, the scale functions of G and H:=G(K) are related by s
H
∣
G
=s
G
[
K
:ℚ
p
]. More generally, we clarify the relations between the scale function of
a p-adic Lie group and the scale functions of its closed subgroups and Hausdorff quotients.
Received: 20 February 1997; Revised version: 18 May 1998 相似文献
18.
19.
Automorphism groups of Weyl-type algebras 总被引:2,自引:0,他引:2
Let F be a field of characteristic 0, be n commuting variables over F, and be the field of all rational functions. Let . We have the simple Weyl type algebra . In this paper, the automorphism group of the associative algebra and the automorphism group of the Lie algebra are determined,
and it is proved that .
Received: 4 October 2001 / Revised version: 5 November 2001 相似文献
20.
Jörg Wensch 《Numerische Mathematik》2001,89(3):591-604
Summary. The numerical solution of differential equations on Lie groups by extrapolation methods is investigated. The main principles
of extrapolation for ordinary differential equations are extended on the general case of differential equations in noncommutative
Lie groups. An asymptotic expansion of the global error is given. A symmetric method is given and quadratic asymptotic expansion
of the global error is proved. The theoretical results are verified by numerical experiments.
Received September 27, 1999 / Revised version received February 14, 2000 / Published online April 5, 2001 相似文献