共查询到20条相似文献,搜索用时 46 毫秒
1.
V. D. Lyakhovsky 《Theoretical and Mathematical Physics》2006,148(1):968-979
In accordance with the quantum duality principle, the twisted algebra
is equivalent to the quantum group
and has two preferred bases: one inherited from the universal enveloping algebra
and the other generated by coordinate functions of the dual Lie group
. We show howthe transformation
can be explicitly obtained for any simple Lie algebra and a factorable chain
of extended Jordanian twists. In the algebra
, we introduce a natural vector grading
, compatible with the adjoint representation of the algebra. Passing to the dual-group coordinates allows essentially simplifying
the costructure of the deformed Hopf algebra
, considered as a quantum group
. The transformation
can be used to construct new solutions of the twist equations. We construct a parameterized family of extended Jordanian
deformations
and study it in terms of
; we find new realizations of the parabolic twist.
Dedicated to the birthday of my teacher, Yurii Novozhilov
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 148, No. 1, pp. 112–125, July, 2006. 相似文献
2.
Let E be a non empty set, let P : = E × E,
:= {x × E|x ∈ E},
:= {E × x|x ∈ E}, and
:= {C ∈ 2
P
|∀X ∈
: |C ∩ X| = 1} and let
. Then the quadruple
resp.
is called chain structure resp. maximal chain structure. We consider the maximal chain structure
as an envelope of the chain structure
. Particular chain structures are webs, 2-structures, (coordinatized) affine planes, hyperbola structures or Minkowski planes.
Here we study in detail the groups of automorphisms
,
,
,
related to a maximal chain structure
. The set
of all chains can be turned in a group
such that the subgroup
of
generated by
the left-, by
the right-translations and by ι the inverse map of
is isomorphic to
(cf. (2.14)). 相似文献
3.
José M. Isidro 《Central European Journal of Mathematics》2007,5(3):512-522
Let G be the Banach-Lie group of all holomorphic automorphisms of the open unit ball
in a J*-algebra
of operators. Let
be the family of all collectively compact subsets W contained in
. We show that the subgroup F ⊂ G of all those g ∈ G that preserve the family
is a closed Lie subgroup of G and characterize its Banach-Lie algebra. We make a detailed study of F when
is a Cartan factor.
相似文献
4.
In this paper we define partially ordered quasi-uniform spaces (X,
, ≤) (PO-quasi-uniform spaces) as those space with a biconvex quasi-uniformity
on the poset (X, ≤) and give a construction of a (transitive) biconvex compatible quasi-uniformity on a partially ordered topological space
when its topology satisfies certain natural conditions. We also show that under certain conditions on the topology
of a PO-quasi-uniform space (X,
, ≤), the bicompletion
of (X,
) is also a PO-quasi-uniform space (
, ⪯) with a partial order ⪯ on
that extends ≤ in a natural way.
相似文献
5.
We construct the trajectory attractor
of a three-dimensional Navier--Stokes system with exciting force
. The set
consists of a class of solutions to this system which are bounded in
, defined on the positive semi-infinite interval
of the time axis, and can be extended to the entire time axis
so that they still remain bounded-in-
solutions of the Navier--Stokes system. In this case any family of bounded-in-
solutions of this system comes arbitrary close to the trajectory attractor
. We prove that the solutions
are continuous in t if they are treated in the space of functions ranging in
. The restriction of the trajectory attractor
to
,
, is called the global attractor of the Navier--Stokes system. We prove that the global attractor
thus defined possesses properties typical of well-known global attractors of evolution equations. We also prove that as
the trajectory attractors
and the global attractors
of the
-order Galerkin approximations of the Navier--Stokes system converge to the trajectory and global attractors
and
, respectively. Similar problems are studied for the cases of an exciting force of the form
depending on time
and of an external force
rapidly oscillating with respect to the spatial variables or with respect to time
. 相似文献
6.
Dorothee Schueth 《Geometriae Dedicata》2004,105(1):77-83
A nonflat Einstein solvmanifold (
, g) is said to be of standard type if in the associated metric Lie algebra
, the orthogonal complement
of the derived algebra is Abelian. It is an open question whether the standard condition is automatically satisfied for all
nonflat Einstein solvmanifolds. We derive certain properties of the metric Lie algebra
of a nonflat Einstein solvmanifold (
, g) under the assumption
. In particular, we obtain some new sufficient conditions which imply standard type. 相似文献
7.
T. Levasseur 《Transformation Groups》1998,3(4):337-353
Let
u
be a compact Lie algebra and let
u
be its complexification. Let ζ−1/2 be the inverse on the set of regular elements of
u
of a square root of the discriminant of
. Generalizing a result of W. Lichtenstein in the case
u
=
(n, ℂ) or
(nℝ), we prove that ∂(q).ζ1/2 is non zero for all harmonic polynomialsq ∈S(
) \ {0}. This fact is deduced from results about equivariantD-modules supported on the nilpotent cone of
. 相似文献
8.
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
9.
Friedrich W. Bauer 《Journal of Mathematical Sciences》2008,148(2):175-191
In a category with homotopy
(Definition 1.1), one can define a natural concept of (co)fibrations and weak equivalences (Sec. 2) such that some properties
of a closed model category hold. If
is a complete and cocomplete category (with respect to finite limits) with simplicial homotopy (Definition 1.3), one achieves a full closed model structure in
(Theorem 4.6). For each category with homotopy
, there exists a category with simplicial homotopy
(see Sec. 5) (the simplicial envelope of
). If
is already a complete category with simplicial homotopy, then
is Quillen equivalent to
(Theorem 5.9).
__________
Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 41, Topology
and Its Applications, 2006. 相似文献
10.
Götz Brunner 《Israel Journal of Mathematics》1972,12(3):306-313
In the definition ofCW-complexes, the one-point spaceP, respectively the spaceP∪* with basepoint *, play the roll of the only “building-stone”. Let
be a family of compact spaces. Then the definition of a generalizedCW-complex over
is obtained from the definition of aCW-complex by replacingP by the spaces of
and formation of the mapping cone by a slightly modified construction. LetCW
* denote the category of all pointed spaces which have the homotopy type of a generalizedCW-complex over
. If
, thenCW
* is the category of all pointedCW-spaces.CW
* is closed under the formation of direct sums and of mapping cones, cylinders and tori, and is formally characterized as
the smallest such subcategory of Top * containing the spaces W∪*,
. Following the methods of E. H. Brown, it is proved, that any half exact homotopy functor onCW
* is representable, and any cohomology theory onCW
is naturally equivalent to the cohomology theory of an Ω-spectrum; for example, the singular cohomo logy is representable
onCW
for any family
of compact spaces.
相似文献
11.
Dong Zhe 《Czechoslovak Mathematical Journal》2006,56(2):287-298
In this paper we investigate finite rank operators in the Jacobson radical
of Alg(
), where
are nests. Based on the concrete characterizations of rank one operators in Alg(
) and
, we obtain that each finite rank operator in
can be written as a finite sum of rank one operators in
and the weak closure of
equals Alg(
) if and only if at least one of
is continuous. 相似文献
12.
Milan Jasem 《Mathematica Slovaca》2007,57(2):107-118
In the paper isometries in pseudo MV-algebras are investigated. It is shown that for every isometry f in a pseudo MV-algebra
= (A, ⊕, −, ∼, 0, 1) there exists an internal direct decomposition
of
with
commutative such that
and
for each x ∈ A.
On the other hand, if
is an internal direct decomposition of a pseudo MV-algebra
= (A, ⊕, −, ∼, 0, 1) with
commutative, then the mapping g: A → A defined by
is an isometry in
and
.
相似文献
13.
V. Yu. Popov 《Algebra and Logic》2005,44(1):46-54
There exist independently based semigroup varieties
and
,
, such that
has no cover in the interval [
;
].Translated from Algebra i Logika, Vol. 44, No. 1, pp. 81–96, January–February, 2005. 相似文献
14.
The following assertion is proved. Let
be the set of integers the number of the prime power of which is
. Let
be the size of
. Then for each irrational
, uniformly in
, \begin{equation*} \frac{1}{\pi_k(x)} \bigg|\sum _{\alul{n\le x}{n\in\cN_k}} f(n) e^{2\pi in\alpha}\bigg|\to 0, \end{equation*}
where
is an arbitrary multiplicative function with
,
is a positive constant.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
15.
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
16.
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
17.
Kazem Khashyarmanesh 《Archiv der Mathematik》2007,88(5):413-418
Let (
) be a commutative Noetherian local ring with non-zero identity,
an ideal of R and M a finitely generated R-module with
. Let D(–) := Hom
R
(–, E) be the Matlis dual functor, where
is the injective hull of the residue field
. We show that, for a positive integer n, if there exists a regular sequence
and the i-th local cohomology module H
i
a
(M) of M with respect to
is zero for all i with i > n then
The author was partially supported by a grant from Institute for Studies in Theoretical Physics and Mathematics (IPM) Iran
(No. 85130023).
Received: 9 August 2006 相似文献
18.
A CDCSL algebra is a reflexive operator algebra with completely distributive and commutative subspace lattice. In this paper,
we show, for a weakly closed linear subspace
of a CDCSL algebra
, that
is a Lie ideal if and only if
for all invertibles A in
, and that
is a Jordan ideal if and only if it is an associative ideal. 相似文献
19.
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
20.
A family of transitive modular Lie superalgebras with depth one 总被引:1,自引:0,他引:1
Wen-de LIU~ 《中国科学A辑(英文版)》2007,50(10):1451-1466
The embedding theorem is established for Z-graded transitive modular Lie superalgebras g=(?)satisfying the conditions: (i)g0(?)(g-1)and g0-module g-1 is isomorphic to the natural(?)(g-1)-module; (ii)dim g1=2/3n(2n~2 1),where n=1/2dim g-1. In particular,it is proved that the finite-dimensional simple modular Lie superalgebras satisfying the conditions above are isomorphic to the odd Hamiltonian superalgebras.The restricted Lie superalgebras are also considered. 相似文献