共查询到20条相似文献,搜索用时 15 毫秒
1.
Sverre O. Smalø 《Milan Journal of Mathematics》2008,76(1):135-164
The purpose of this note is to give a fast introduction to some problems of homological and geometrical nature related to
finite-dimensional representations of finitely generated, and especially, finite-dimensional algebras over a field. Some of
these results can also be extended to the situation where the field is not algebraically closed, and some of the results can
even be extended to the situation where one is considering algebras over a commutative artin ring. For the results which hold
true in the most general situation the proofs become most elegant since they depend on using length arguments only and thereby
forgetting about the nature of a field altogether.
Received: July 2007 相似文献
2.
Donald Sarason 《Integral Equations and Operator Theory》2008,61(2):281-298
This partly expository article develops the basic theory of unbounded Toeplitz operators on the Hardy space H
2, with emphasis on operators whose symbols are not square integrable. Unbounded truncated Toeplitz operators on coinvariant
subspaces of H
2 are also studied.
In memory of Paul R. Halmos 相似文献
3.
Sorin Dăscălescu 《Archiv der Mathematik》2008,91(3):212-217
We describe all group gradings on the diagonal algebra k
n
, where k is an arbitrary field.
Received: 21 January 2008 相似文献
4.
We note a sharp embedding of the Besov space into exponential classes and prove entropy estimates for the compact embedding of subclasses with logarithmic smoothness,
considered by Kashin and Temlyakov.
A.S. was supported in part by the National Science Foundation grant 0652890. 相似文献
5.
Xiao-Wu Chen 《Archiv der Mathematik》2009,93(1):29-35
Gentle and Todorov proved that in an abelian category with enough projective objects, the extension subcategory of two covariantly
finite subcategories is covariantly finite. We give an example to show that Gentle–Todorov’s theorem may fail in an arbitrary
abelian category; however we prove a triangulated version of Gentle–Todorov’s theorem which holds for arbitrary triangulated
categories; we apply Gentle–Todorov’s theorem to obtain short proofs of a classical result by Ringel and a recent result by
Krause and Solberg.
This project is partially supported by China Postdoctoral Science Foundation (No.s 20070420125 and 200801230). The author
also gratefully acknowledges the support of K. C. Wong Education Foundation, Hong Kong. 相似文献
6.
We consider a finite dimensional k-algebraA and associate to each tilting module a cone in the Grothendieck groupK
0 of finitely generated A-modules. We prove that the set of cones associated to tilting modules of projective dimension at
most one defines a, not necessarily finite, fan Σ(A). IfA is of finite global dimension, the fan Σ(A) is smooth. Moreover, using the cone of a tilting module, we can associate a volume
to each tilting module. Using the fan and the volume, we obtain new proofs for several classical results; we obtain certain
convergent sums naturally associated to the algebraA and obtain criteria for the completeness of a list of tilting modules. Finally, we consider several examples.
Dedicated to O. Riemenschneider on the occasion of his 65th birthday 相似文献
7.
C. Buşe A. D. R. Choudary S. S. Dragomir M. S. Prajea 《Integral Equations and Operator Theory》2008,61(3):325-340
A result of Barbashin ([1], [15]) states that an exponentially bounded evolution family defined on a Banach space and satisfying some measurability conditions is uniformly exponentially stable if and only if for
some 1 ≤ p < ∞, we have that:
Actually the Barbashin result was formulated for non-autonomous differential equations in the framework of finite dimensional
spaces. Here we replace the above ”uniform” condition be a ”strong” one.
Among others we shall prove that the evolution family is uniformly exponentially stable if there exists a non-decreasing function with for all r > 0 such that for each , one has:
In particular, the family U is uniformly exponentially stable if and only if for some 0 < p < ∞ and each , the inequality
is fulfilled. The latter result extends a similar one from the recent paper [4]. Related results for periodic evolution families
are also obtained.
相似文献
8.
Non-group-theoretical semisimple Hopf algebras from group actions on fusion categories 总被引:1,自引:0,他引:1
Dmitri Nikshych 《Selecta Mathematica, New Series》2008,14(1):145-161
Given an action of a finite group G on a fusion category we give a criterion for the category of G-equivariant objects in to be group-theoretical, i.e., to be categorically Morita equivalent to a category of group-graded vector spaces. We use
this criterion to answer affirmatively the question about existence of non-group-theoretical semisimple Hopf algebras asked
by P. Etingof, V. Ostrik, and the author in [7]. Namely, we show that certain /2-equivariantizations of fusion categories constructed by D. Tambara and S. Yamagami [26] are equivalent to representation
categories of non-group-theoretical semisimple Hopf algebras. We describe these Hopf algebras as extensions and show that
they are upper and lower semisolvable.
相似文献
9.
Constantin Buşe Mihail Megan Manuela-Suzy Prajea Petre Preda 《Integral Equations and Operator Theory》2007,59(4):491-500
Among others we shall prove that an exponentially bounded evolution family U = {U(t, s)}
t≥s≥0 of bounded linear operators acting on a Banach space X is uniformly exponentially stable if and only if there exists q
[1, ∞) such that
This result seems to be new even in the finite dimensional case and it is the strong variant of an old result of E. A. Barbashin
([1]Theorem 5.1).
The first author was partially supported by the CNCSIS’s grant no. 546/2006. 相似文献
10.
Boo Rim Choe Hyungwoon Koo Michael Stessin 《Integral Equations and Operator Theory》2009,63(4):501-520
We obtain new characterizations of Carleson measures via uniform boundedness of BMO norms of certain mass functions associated
with the given measure in a natural way.
This research was performed during M. Stessin’s visit to Korea University. He thanks the Mathematics Department of Korea University
and the “Brain Pool” program for their hospitality and support. The first two authors were supported by the Korea Research
Foundation Grant funded by the Korean Government (KRF-2008-314-C00012). 相似文献
11.
Thomas Schmidt 《NoDEA : Nonlinear Differential Equations and Applications》2009,16(1):109-129
We consider multi-dimensional variational integrals
where the integrand f is a strictly convex function of its last argument. We give an elementary proof for the partial -regularity of minimizers of F. Our approach is based on the method of A-harmonic approximation, avoids the use of Gehring’s lemma, and establishes partial regularity with the optimal H?lder exponent
α in a single step.
相似文献
12.
Thomas Weigel 《Archiv der Mathematik》2005,85(1):55-69
Any morphism
of profinite groups has maximal ℓ-Frattini quotients
is an ℓ-Frattini extension and β is a surjective morphism of profinite groups for which every minimal finite non-trivial ℓ-embedding problem is not weakly solvable. In this paper the case is studied where Ĝ
Ĝ is a weakly-orientable ℓ-Poincaré duality group of dimension 2 and where A is a finite group whose order is divisible by ℓ. This analysis can be applied for the study of modular towers (Theorem A, Remark 1.2). It is shown that the existence of finite maximal ℓ-Frattini quotients is controlled by an integer r
ℓ(A) (Theorem B). In the final section we study properties of the morphism ϕ which imply that for every maximal ℓ-Frattini quotient (π, β), the profinite group B itself is a weakly-orientable ℓ-Poincaré duality group of dimension 2 (Theorem C).Received: 17 January 2005; revised: 21 March 2005 相似文献
13.
In this paper we characterize when the path ring associated to a quiver is Gorenstein (in the sense of Iwanaga [9]). Then,
by using the notion of a Gorenstein category (cf. [2]), we extend the classes of quivers whose corresponding category of representations
has finite Gorenstein global dimension. This extension includes non-noetherian quivers.
E. E., S.E., and J.R.G.R., partially supported by the DGI MTM2005-03227.
Estrada’s work was supported by a MEC/Fulbright grant from the Spanish Secretaría de Estado de Universidades e Investigación
del Ministerio de Educación y Ciencia.
Received: 28 February 2006 相似文献
14.
Hermitean Clifford analysis is a recent branch of Clifford analysis, refining the Euclidean case; it focusses on the simultaneous
null solutions, called Hermitean monogenic functions, of two complex Dirac operators which are invariant under the action
of the unitary group. The specificity of the framework, introduced by means of a complex structure creating a Hermitean space,
forces the underlying vector space to be even dimensional. Thus, any Hilbert convolution kernel in should originate from the non-tangential boundary limits of a corresponding Cauchy kernel in . In this paper we show that the difficulties posed by this inevitable dimensional jump can be overcome by following a matrix
approach. The resulting matrix Hermitean Hilbert transform also gives rise, through composition with the matrix Dirac operator,
to a Hermitean Hilbert–Dirac convolution operator “factorizing” the Laplacian and being closely related to Riesz potentials.
Received: October, 2007. Accepted: February, 2008. 相似文献
15.
On the setting of the half-space we introduce the Schatten-Herz classes of Toeplitz operators and obtain characterizations
for positive Toeplitz operators to belong to those classes. We also prove results concerning the boundedness and compactness
of Toeplitz operators with Herz symbols. Such a study has been recently done on the ball. At a critical step of the proofs
we employ a much simplified argument to extend the range of parameters for Herz spaces on which the Berezin transform is bounded.
Our results show not only that most of results on the ball continue to hold, but also that there is some pathology caused
by the unboundedness of the domain.
The first author was in part supported by a Korea University Grant(2007), the second author was in part supported by Hanshin
University Research Grant, and both authors were in part supported by KOSEF(R01-2003-000-10243-0). 相似文献
16.
Eugene Shargorodsky 《Integral Equations and Operator Theory》2007,57(1):127-132
We establish a sufficient condition for a point to belong to the essential spectrum of a Toeplitz operator with a bounded
measurable coefficient. This condition uses geometric information on the cluster values of the coefficient. 相似文献
17.
M. Rovinsky 《Selecta Mathematica, New Series》2009,15(2):343-376
Let G be the automorphism group of an extension of algebraically closed fields of characteristic zero of transcendence degree n, 1 ≤ n ≤ ∞. In this paper we
The study of open subgroups is motivated by the study of (the stabilizers of) smooth representations undertaken in [R1, R3].
The functor Γ is an analogue of the global sections functor on the category of sheaves on a smooth proper algebraic variety.
Another result is that ‘interesting’ semilinear representations are ‘globally generated’.
相似文献
• | construct some maximal closed non-open subgroups Gv, and some (all, in the case of countable transcendence degree) maximal open proper subgroups of G; |
• | describe, in the case of countable transcendence degree, the automorphism subgroups over the intermediate subfields (a question of Krull, [K2, §4, question 3b)]); |
• | construct, in the case n = ∞, a fully faithful subfunctor ( − )v of the forgetful functor from the category of smooth representations of G to the category of smooth representations of Gv; |
• | construct, using the functors ( − )v, a subfunctor Γ of the identity functor on , coincident (via the forgetful functor) with the functor Γ on the category of admissible semilinear representations of G constructed in [R3] in the case n = ∞ and . |
18.
Alberto Damiano 《Advances in Applied Clifford Algebras》2007,17(3):343-355
This paper is a short report on the generalization of some results of our previous paper [12] to the case of spin j/2 Dirac operators in real dimension three for arbitrary odd integer j. We use an explicit formula for the local expression of such operators to study their algebraic properties, construct the
compatibility conditions of the overdetermined system associated to the operator in several spatial variables, and we prove
that its associated algebraic complex, dual do the BGG sequence coming from representation theory, has substantially the same
pattern as the Cauchy-Fueter complex.
The author is a member of the Eduard Čech Center and his research is supported by the relative grants. 相似文献
19.
We discuss the optimality of a sufficient condition from [12] for a point to belong to the essential spectrum of a Toeplitz
operator with a bounded measurable coefficient. Our approach is based on a new sufficient condition for a composition of a
Muckenhoupt weight with a Blaschke product to belong to the same Muckenhoupt class.
The first author was partially supported by CONACYT project U46936-F, Mexico. 相似文献
20.
Josef Daněček Eugen Viszus 《NoDEA : Nonlinear Differential Equations and Applications》2009,16(2):189-211
We discuss the interior C
0,γ-everywhere regularity for minimizers of quasilinear functionals of the type
where VMO dependence on the variable x and continuous dependence on the variable u are supposed.
J. Daněček was supported by the research project MSM 0021630511, E. Viszus was supported by the research project Slovak Grant
Agency No.1/0098/08. 相似文献