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1.
Lutz Strüngmann 《Archiv der Mathematik》2006,86(3):193-204
Let R be a unital associative ring and
two classes of left R-modules. In this paper we introduce the notion of a
In analogy to classical cotorsion pairs as defined by Salce [10], a pair
of subclasses
and
is called a
if it is maximal with respect to the classes
and the condition
for all
and
Basic properties of
are stated and several examples in the category of abelian groups are studied.
Received: 17 March 2005 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.
4.
In our previous work, we introduced a bijection between the elements of the crystal base of the negative (resp. positive)
part of the quantized universal enveloping algebra
of a Kac–Moody algebra
that are fixed by a diagram automorphism and the elements of the crystal base of the negative (resp. positive) part of the
quantized universal enveloping algebra
of the orbit Lie algebra
of
. In this paper, we prove that this bijection commutes with the *-operation. As an application of this result we show that
there exists a canonical bijection between the elements ℬ0(λ) of the crystal base ℬ(λ) of an extremal weight module of extremal weight λ over
that are fixed by a diagram automorphism and the elements of the crystal base
of an extremal weight module of extremal weight
over
, if the crystal graph of
is connected.
Presented by P. Littelmann
Mathematics Subject Classifications (2000) Primary: 17B37, 17B10; secondary: 81R50. 相似文献
5.
M. A. Bastos C. A. Fernandes Yu. I. Karlovich 《Integral Equations and Operator Theory》2006,55(1):19-67
We establish a symbol calculus for the C*-subalgebra
of
generated by the operators of multiplication by slowly oscillating and piecewise continuous functions and the operators
where
is the Cauchy singular integral operator and
The C*-algebra
is invariant under the transformations
where Uz is the rotation operator
Using the localtrajectory method, which is a natural generalization of the Allan-Douglas local principle to nonlocal type
operators, we construct symbol calculi and establish Fredholm criteria for the C*-algebra
generated by the operators
and
for the C*-algebra
generated by the operators
and
and for the C*-algebra
generated by the algebras
and
The C*-algebra
can be considered as an algebra of convolution type operators with piecewise slowly oscillating coefficients and shifts acting
freely. 相似文献
6.
Birkhoff coordinates for KdV on phase spaces of distributions 总被引:1,自引:0,他引:1
The purpose of this paper is to extend the construction of Birkhoff coordinates for the KdV equation from the phase space
of square integrable 1-periodic functions with mean value zero to the phase space
of mean value zero distributions from the Sobolev space
endowed with the symplectic structure
More precisely, we construct a globally defined real-analytic symplectomorphism
where
is a weighted Hilbert space of sequences
supplied with the canonical Poisson structure so that the KdV Hamiltonian for potentials in
is a function of the actions
alone. 相似文献
7.
The peak algebra
is a unital subalgebra of the symmetric group algebra, linearly spanned by sums of permutations with a common set of peaks.
By exploiting the combinatorics of sparse subsets of [n−1] (and of certain classes of compositions of n called almost-odd and thin), we construct three new linear bases of
. We discuss two peak analogs of the first Eulerian idempotent and construct a basis of semi-idempotent elements for the peak
algebra. We use these bases to describe the Jacobson radical of
and to characterize the elements of
in terms of the canonical action of the symmetric groups on the tensor algebra of a vector space. We define a chain of ideals
of
, j = 0,...,
, such that
is the linear span of sums of permutations with a common set of interior peaks and
is the peak algebra. We extend the above results to
, generalizing results of Schocker (the case j = 0).
Aguiar supported in part by NSF grant DMS-0302423
Orellana supported in part by the Wilson Foundation 相似文献
8.
Let R be a commutative ring. An Azumaya coring consists of a couple
, with S a faithfully flat commutative R-algebra, and an S-coring
satisfying certain properties. If S is faithfully projective, then the dual of
is an Azumaya algebra. Equivalence classes of Azumaya corings form an abelian group, called the Brauer group of Azumaya corings.
This group is canonically isomorphic to the second flat cohomology group. We also give algebraic interpretations of the second
Amitsur cohomology group and the first Villamayor–Zelinsky cohomology group in terms of corings. 相似文献
9.
The main result in Cossidente and Siciliano (J. Number Theory, Vol. 99 (2003) pp. 373–382) states that if a Singer subgroup of PGL(3,q) is an automorphism group of a projective, geometric
irreducible, non-singular plane algebraic curve
then either
or
. In the former case
is projectively equivalent to the curve
with equation Xq+1Y+Yq+1+X=0 studied by Pellikaan. Furthermore, the curve
has a very nice property from Finite Geometry point of view: apart from the three distinguished points fixed by the Singer
subgroup, the set of its
-rational points can be partitioned into finite projective planes
. In this paper, the full automorphism group of such curves is determined. It turns out that
is the normalizer of a Singer group in
. 相似文献
10.
Yury M. Arlinskiĭ Seppo Hassi Henk S. V. de Snoo 《Complex Analysis and Operator Theory》2009,3(1):19-56
Passive systems with and as an input and output space and as a state space are considered in the case that the main operator on the state space is normal. Basic properties are given
and a general unitary similarity result involving some spectral theoretic conditions on the main operator is established.
A passive system with is said to be quasi-selfadjoint if ran . The subclass of the Schur class is the class formed by all transfer functions of quasi-selfadjoint passive systems. The subclass is characterized and minimal passive quasi-selfadjoint realizations are studied. The connection between the transfer function
belonging to the subclass and the Q-function of T is given.
Received: December 16, 2007., Accepted: March 4, 2008. 相似文献
11.
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
12.
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
13.
Niels Jakob Laustsen 《K-Theory》2001,23(2):115-127
We prove that the K-groups of the Banach algebra
of bounded, linear operators on the pth James space
, where 1 < p < , are given by
and
. Moreover, for each Banach space
and each non-zero, closed ideal
contained in the ideal of inessential operators, we show that
and
. This enables us to calculate the K-groups of
for each Banach space
which is a direct sum of finitely many James spaces and
-spaces. 相似文献
14.
If E is a separable symmetric sequence space with trivial Boyd indices and
is the corresponding ideal of compact operators, then there exists a C1-function fE, a self-adjoint element
and a densely defined closed symmetric derivation δ on
such that
, but
相似文献
15.
Let
be an
-filtered category in the sense of Karoubi. This is the categorical analogue of an ideal
in a ring
. Pedersen and Weibel constructed a fibration of K-theory spectra associated with the sequence
. We present a new easier proof based on Waldhausen' generic fibration. 相似文献
16.
Let
be a compact Riemannian manifold without boundary. In this paper, we consider the first nonzero eigenvalue of the p-Laplacian
and we prove that the limit of
when
is 2/d(M), where d(M) is the diameter of M. Moreover, if
is an oriented compact hypersurface of the Euclidean space
or
, we prove an upper bound of
in terms of the largest principal curvature κ over M. As applications of these results, we obtain optimal lower bounds of d(M) in terms of the curvature. In particular, we prove that if M is a hypersurface of
then:
.
Mathematics Subject Classifications (2000): 53A07, 53C21. 相似文献
17.
We study the Yangians
associated with the simple Lie algebras
of type B, C or D. The algebra
can be regarded as a quotient of the extended Yangian
whose defining relations are written in an R-matrix form. In this paper we are concerned with the algebraic structure and representations of the algebra
. We prove an analog of the Poincaré–Birkhoff–Witt theorem for
and show that the Yangian
can be realized as a subalgebra of
. Furthermore, we give an independent proof of the classification theorem for the finite-dimensional irreducible representations
of
which implies the corresponding theorem of Drinfeld for the Yangians
. We also give explicit constructions for all fundamental representation of the Yangians.
Communicated by Petr Kulish
Dedicated to Daniel Arnaudon
Submitted: November 22, 2005; Accepted: February 1, 2006 相似文献
18.
Antonio G. García Miguel A. Hernández-Medina 《Mediterranean Journal of Mathematics》2005,2(3):345-356
Let
be a symmetric operator with compact resolvent defined in a Hilbert space
For any fixed
we consider an entire
function Ka which involves the resolvent of
Associated with Ka we obtain, by duality in
a Hilbert space
of entire functions which becomes a De Branges space of entire functions. This property provides a characterization of
regardless of the anti-linear mapping which has
as its range space. There exists also a sampling formula allowing to recover any function in
from its samples at the sequence of eigenvalues of
This work has been supported by the grant BFM2003–01034 from the D.G.I. of the Spanish Ministerio de Ciencia y Tecnología. 相似文献
19.
We show that for a variety
of Heyting algebras the following conditions are equivalent: (1)
is locally finite; (2) the
-coproduct of any two finite
-algebras is finite; (3) either
coincides with the variety of Boolean algebras or finite
-copowers of the three element chain
are finite. We also show that a variety
of Heyting algebras is generated by its finite members if, and only if,
is generated by a locally finite
-algebra. Finally, to the two existing criteria for varieties of Heyting algebras to be finitely generated we add the following
one:
is finitely generated if, and only if,
is residually finite.
Received November 11, 2001; accepted in final form July 25, 2005. 相似文献
20.
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