共查询到20条相似文献,搜索用时 62 毫秒
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.
In this paper, we consider equations of the form
, where
is a function with values in the Hilbert space
, the operator B is symmetric, and the operator A is uniformly positive and self-adjoint in
. The linear operator
generating the C
0-semigroup in the energy space
is associated with this equation. We prove that this semigroup is exponentially stable if the operator B is uniformly positive and the operator A dominates B in the sense of quadratic forms. 相似文献
3.
We consider the Skyrme model using the explicit parameterization of the rotation group
through elements of its algebra. Topologically nontrivial solutions already arise in the one-dimensional case because the fundamental group of
is
. We explicitly find and analyze one-dimensional static solutions. Among them, there are topologically nontrivial solutions with finite energy. We propose a new class of projective models whose target spaces are arbitrary real projective spaces
. 相似文献
4.
Stefano Cavallaro 《Algebras and Representation Theory》2000,3(2):175-186
Let
be an Abelian unital C
*-algebra and let
denote its Gelfand spectrum. We give some necessary and sufficient conditions for a nondegenerate representation of
to be unitarily equivalent to a representation in which the elements of
act multiplicatively, by their Gelfand transforms, on a space L
2(
,), where is a positive measure on the Baire sets of
. We also compare these conditions with the multiplicity-free property of a representation. 相似文献
5.
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
6.
Ján Jakubík 《Czechoslovak Mathematical Journal》2002,52(3):651-663
Let Int
be the lattice of all intervals of an MV-algebra
. In the present paper we investigate the relations between direct product decompositions of
and (i) the lattice Int
, or (ii) 2-periodic isometries on
, respectively. 相似文献
7.
Let R be a homogeneous ring over an infinite field, IR a homogeneous ideal, and
I an ideal generated by s forms of degrees d
1,...,d
s
so that codim(
:I)s. We give broad conditions for when the Hilbert function of R/
or of R/(
:I) is determined by I and the degrees d
1,...,d
s
. These conditions are expressed in terms of residual intersections of I, culminating in the notion of residually S
2 ideals. We prove that the residually S
2 property is implied by the vanishing of certain Ext modules and deduce that generic projections tend to produce ideals with this property. 相似文献
8.
Avishay Vaknin 《K-Theory》2001,24(1):57-68
For a small triangulated category
, Bass's K
1 group
is described, and the theorem of the heart is proved. We define the determinant map from
to Neeman's
, and we compute this map when
is the derived category of an Abelian category
. 相似文献
9.
Cocalibrated G2-manifolds are seven-dimensional Riemannian manifolds with a distinguished 3-form which is coclosed. For such a manifold M, S. Salamon in Riemannian Geometry and Holonomy Groups (Longman, 1989) defined a differential complex
related with the G2-structure of M.In this paper we study the cohomology
of this complex;it is treated as an analogue of a Dolbeault cohomologyof complex manifolds. For compact G2-manifoldswhose holonomy group is a subgroup of G2 special propertiesare proved. The cohomology
of any cocalibrated G2-nilmanifold \K is also studied. 相似文献
10.
11.
Aderemi Kuku 《K-Theory》2001,22(4):367-392
Let
be a rational prime,
an exact category. In this article, we define and study for all
, the profinite higher K-theory of
, that is
as well as
, where
is the
-dimensional mod-
Moore space. We study connections between
and prove several
-completeness results involving these and associated groups including the cases where
is the category of finitely generated (resp. finitely generated projective) modules over orders in semi-simple algebras over number fields and p-adic fields. We also define and study continuous K-theory
of orders in p-adic semi-simple algebras and show some connection between the profinite and continuous K-theory of . 相似文献
12.
Let
be a Kac–Moody algebra, U(x,y) be a function defined in
, and a be a constant element of
. We prove that the equation U
xy = [[U,a],U
x] has two symmetry hierarchies connected by a gauge transformation. In particular, the well-known Konno equation appears in the case of the algebra
. The corresponding symmetry hierarchies contain the nonlinear Schrödinger and the Heisenberg magnet equations. 相似文献
13.
D. I. Panyushev 《Functional Analysis and Its Applications》2004,38(1):38-44
Let
be a reductive Lie algebra over an algebraically closed field of characteristic zero and
an arbitrary
-grading. We consider the variety
, which is called the commuting variety associated with the
-grading. Earlier it was proved by the author that
is irreducible, if the
-grading is of maximal rank. Now we show that
is irreducible for
and (E6,F4). In the case of symmetric pairs of rank one, we show that the number of irreducible components of
is equal to that of nonzero non--regular nilpotent G
0-orbits in
. We also discuss a general problem of the irreducibility of commuting varieties. 相似文献
14.
In this paper we show that the support of the codewords of each type in the Kerdock code of length 2m over Z4 form 3-designs for any odd integer
. In particular, twonew infinite families of 3-designs are obtained in this constructionfor any odd integer
. In particular, twonew infinite families of 3-designs are obtained in this constructionfor any odd integer
, whose parameters are
,and
. 相似文献
15.
Wiesław Śliwa 《Czechoslovak Mathematical Journal》2004,54(2):457-463
We prove that any infinite-dimensional non-archimedean Fréchet space E is homeomorphic to
where D is a discrete space with card(D) = dens(E). It follows that infinite-dimensional non-archimedean Fréchet spaces E and F are homeomorphic if and only if dens(E) = dens(F). In particular, any infinite-dimensional non-archimedean Fréchet space of countable type over a field
is homeomorphic to the non-archimedean Fréchet space
. 相似文献
16.
We construct a metric space of set functions (
, d) such that a sequence {P
n} of Borel probability measures on a metric space (
, d*) satisfies the full Large Deviation Principle (LDP) with speed {a
n} and good rate function I if and only if the sequence
converges in (
, d) to the set function e
–I
. Weak convergence of probability measures is another special case of convergence in (
, d). Properties related to the LDP and to weak convergence are then characterized in terms of (
, d). 相似文献
17.
We present a connection between
-algebras and Yangians in the case of gl(N) algebras, as well as for twisted Yangians and super-Yangians. We illustrate this connection, which allows constructing an R-matrix for the
-algebras and classifying their finite-dimensional irreducible representations, in the framework of the nonlinear Schrödinger equation in 1+1 dimensions. 相似文献
18.
H. P. A. Künzi S. Romaguera M. A. Sánchez-Granero 《Czechoslovak Mathematical Journal》2004,54(1):215-228
We characterize those Tychonoff quasi-uniform spaces
for which the Hausdorff-Bourbaki quasi-uniformity is uniformly locally compact on the family
of nonempty compact subsets of X. We deduce, among other results, that the Hausdorff-Bourbaki quasi-uniformity of the locally finite quasi-uniformity of a Tychonoff space Xis uniformly locally compact on
if and only if Xis paracompact and locally compact. We also introduce the notion of a co-uniformly locally compact quasi-uniform space and show that a Hausdorff topological space is -compact if and only if its (lower) semi-continuous quasi-uniformity is co-uniformly locally compact. A characterization of those Hausdorff quasi-uniform spaces
for which the Hausdorff-Bourbaki quasi-uniformity is co-uniformly locally compact on
is obtained. 相似文献
19.
Chang Jen-Chun Chen Rong-Jaye Hwang Frank K. 《Methodology and Computing in Applied Probability》2001,3(4):379-386
A d-within-consecutive-k-out-of-n system, abbreviated as Con(d, k, n), is a linear system of n components in a line which fails if and only if there exists a set of k consecutive components containing at least d failed ones. So far the fastest algorithm to compute the reliability of Con(d, k, n) is Hwang and Wright's
algorithm published in 1997, where
. In this paper we use automata theory to reduce
to
. For d small or close to k, we have reduced
from exponentially many (in k) to polynomially many. The computational complexity of our final algorithm is
, where
. 相似文献
20.
O. V. Sarafanov 《Journal of Mathematical Sciences》2004,120(2):1195-1239
The C
*-algebra
generated by the operators of pseudodifferential boundary value problems on a manifold
with smooth closed disjoint edges and boundary
is studied. The operators act in the space L
2(
)
L
2(
). The goal of this paper is to describe all (up to an equivalence) irreducible representations of the algebra
Bibliography: 12 titles. 相似文献