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1.
We introduce the notion of the
-prolongation of Lie algebras of differential operators on homogeneous spaces. The
-prolongations are topological invariants that coincide with one-dimensional cohomologies of the corresponding Lie algebras in the case where V is a homogeneous space. We apply the obtained results to the spaces S
1 (the Virasoro algebra) and
. 相似文献
2.
David A. Richter 《Acta Appl Math》2001,66(1):41-65
Starting from the commutation relations in a complex semisimple Lie algebra
, one may obtain a space
of vector fields on Euclidean space such that
and
are isomorphic when
is equipped with the usual Lie bracket between vector fields and the isotropy subalgebra of
is a Borel subalgebra
. Furthermore, one may adjoin to the vector fields in
multiplication operators to obtain an
-parameter family of distinct presentations of
as spaces of differential operators, where
is the dual of a Cartan subalgebra. Some of these presentations will preserve a space of polynomials on Euclidean space, and, in fact, all the finite-dimensional representations of
can be presented in this way. All of this is carried out explicitly for arbitrary
. In doing so, one discovers there is a Lie group of diffeomorphisms of the unipotent subgroup N complementary to B which acts on these presentations and preserves a certain notion of weight. 相似文献
3.
Dražen Adamović 《Algebras and Representation Theory》2004,7(4):457-469
Let
be the affine Lie algebra associated to the simple finite-dimensional Lie algebra
. We consider the tensor product of the loop
-module
associated to the irreducible finite-dimensional
-module V() and the irreducible highest weight
-module L
k,. Then L
k, can be viewed as an irreducible module for the vertex operator algebra M
k,0. Let A(L
k,) be the corresponding
-bimodule. We prove that if the
-module
is zero, then the
-module
is irreducible. As an example, we apply this result on integrable representations for affine Lie algebras. 相似文献
4.
Factorizations of One-Generated Composition Formations 总被引:2,自引:0,他引:2
A non-empty formation
of finite groups is said to be solubly saturated, or we call it a composition formation, if every finite group G having a normal subgroup N such that
belongs to
. An intersection of all composition formations containing a given group G is denoted cformG. Conditions are described under which
has the form
, where
. 相似文献
5.
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
6.
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
7.
Let
be a reductive Lie algebra over C. We say that a
-module M is a generalized Harish-Chandra module if, for some subalgebra
, M is locally
-finite and has finite
-multiplicities. We believe that the problem of classifying all irreducible generalized Harish-Chandra modules could be tractable. In this paper, we review the recent success with the case when
is a Cartan subalgebra. We also review the recent determination of which reductive in
subalgebras
are essential to a classification. Finally, we present in detail the emerging picture for the case when
is a principal 3-dimensional subalgebra. 相似文献
8.
We obtain the decomposition of the tensor space
as a module for
, find an explicit formula for the multiplicities of its irreducible summands, and (when n 2k) describe the centralizer algebra
=
(
) and its representations. The multiplicities of the irreducible summands are derangement numbers in several important instances, and the dimension of
is given by the number of derangements of a set of 2k elements. 相似文献
9.
For a Hopf algebra
, we define the structures of differential complexes on two dual exterior Hopf algebras: (1) an exterior extension of
and (2) an exterior extension of the dual algebra
*. The Heisenberg double of these two exterior Hopf algebras defines the differential algebra for the Cartan differential calculus on
. The first differential complex is an analogue of the de Rham complex. When
* is a universal enveloping algebra of a Lie (super)algebra, the second complex coincides with the standard complex. The differential is realized as an (anti)commutator with a BRST operator Q. We give a recursive relation that uniquely defines the operator Q. We construct the BRST and anti-BRST operators explicitly and formulate the Hodge decomposition theorem for the case of the quantum Lie algebra U
q(gl(N)). 相似文献
10.
A. Cossidente J. W. P. Hirschfeld G. Korchmáros F. Torres 《Compositio Mathematica》2000,121(2):163-181
The number N of rational points on an algebraic curve of genus g over a finite field
satisfies the Hasse–Weil bound
. A curve that attains this bound is called maximal. With
and
, it is known that maximalcurves have
. Maximal curves with
have been characterized up to isomorphism. A natural genus to be studied is
and for this genus there are two non-isomorphic maximal curves known when
. Here, a maximal curve with genus g
2 and a non-singular plane model is characterized as a Fermat curve of degree
. 相似文献
11.
We say that
is a ring with duality for simple modules, or simply a DSM-ring, if, for every simple right (left)
-module U, the dual module U* is a simple left (right)
-module. We prove that a semiperfect ring is a DSM-ring if and only if it admits a Nakayama permutation. We introduce the notion of a monomial ideal of a semiperfect ring and study the structure of hereditary semiperfect rings with monomial ideals. We consider perfect rings with monomial socles. 相似文献
12.
For semigroups (e
tA
)
t0 of operators on a Hilbert space, we give conditions guaranteeing trace estimates of the polynomial type
0$$
" align="middle" border="0">
, where
denotes the trace class. As an application we present higher order analogues of results due to E.B. Davies, B. Simon and M. van den Berg of the type
0$$
" align="middle" border="0">
, for certain unbounded domains
, e.g. spiny urchin domains. 相似文献
13.
A renormalization group transformation R
1 has a single stable point
in the space of the analytic circle homeomorphisms with a single cubic critical point and with the rotation number
(the golden mean). Let a homeomorphism T be the C
1-conjugate of
. We let
denote the sequence of distribution functions of the time of the kth entrance to the nth renormalization interval for the homeomorphism T. We prove that for any
, the sequence
has a finite limiting distribution function
, which is continuous in
, and singular on the interval [0,1]. We also study the sequence
for k>1. 相似文献
14.
V. V. Kornienko 《Mathematical Notes》2000,68(5-6):576-587
We study the distribution in the complex plane
of the spectrum of the operator
, generated by the closure in
of the operation
originally defined on smooth functions
with values in a Hilbert space
satisfying the Dirichlet conditions
. Here
and A is a model operator acting in
. Criterial conditions on the parameter
for the eigenfunctions of the operator
to form a complete and minimal system as well as a Riesz basis in the Hilbert space H are given. 相似文献
15.
The 3-local geometry
of the sporadic simple group Co1 has been known to have a cover
with a flag-transitive automorphism group which is a nonsplit extension of an elementary Abelian 2-group of rank 24 (the Leech lattice modulo 2) by Co1. It was conjectured that
was simply connected. We disprove this conjecture by constructing a double cover
of
. The automorphism group of
is of the shape
. However, it is not isomorphic to the involution centralizer of the Monster sporadic simple group. 相似文献
16.
17.
This article improves results of Hamada, Helleseth and Maekawa on minihypers in projective spaces and linear codes meeting the Griesmer bound.In [10,12],it was shown that any
-minihyper, with
, where
, is the disjoint union of
points,
lines,...,
-dimensional subspaces. For q large, we improve on this result by increasing the upper bound on
non-square, to
non-square,
square,
, and (4) for
square, p prime, p<3, to
. In the case q non-square, the conclusion is the same as written above; the minihyper is the disjoint union of subspaces. When q is square however, the minihyper is either the disjoint union of subspaces, or the disjoint union of subspaces and one subgeometry
. For the coding-theoretical problem, our results classify the corresponding
codes meeting the Griesmer bound. 相似文献
18.
An n-subsetD of a group G of order
is called an affine difference set of G relativeto a normal subgroup N of G of order
if the list of differences
containseach element of G-N exactly once and no elementof N. It is a well-known conjecture that if Dis an affine difference set in an abelian group G,then for every prime p, the Sylow p-subgroupof G is cyclic. In Arasu and Pott [1], it was shownthat the above conjecture is true when
. In thispaper we give some conditions under which the Sylow p-subgroupof G is cyclic. 相似文献
19.
I. L. Bloshanskii 《Analysis Mathematica》2000,26(2):81-98
The problem investigated is to characterize sets E, the sets of unbounded divergence (at each point) of single and multiple Fourier series under condition of convergence of these series to zero at each point of the complement of E.For any nonempty open set B T
N
= [0, 2]
N
, N 1, a Lebesgue integrable function f
0 is constructed which equals zero on the set U = T
N
\ B whose multiple trigonometric Fourier series diverges unboundedly (in the case of summation over squares) at each point of the set
, where
is the closure of the set
, pr(j)
is the orthogonal projection of the set
on the axis Ox
j
, j = 1,...,N. It is also proved that if
, then for any function f equal zero on the set U the multiple trigonometric Fourier series of the function f (in the case of summation over rectangles) converges at each point of the set T
N
\
. 相似文献
20.
M. S. Lyapina 《Journal of Mathematical Sciences》2004,120(2):1109-1116
A bi-Lipschitz continuous mapping of a space X is a bijection
such that
, where
. We write
if f is a Lipschitz (bi-Lipschitz) mapping of X into itself and denote by
the set of all bi-Lipschitz mappings of X that are not isometry. Thus,
if
and blip
. For X we consider a standard Cantor set K on the real line (with standard metric). The main result of this paper is formulated as follows:
where
Bibliography: 2 titles. 相似文献