共查询到20条相似文献,搜索用时 46 毫秒
1.
Fernando Muro 《K-Theory》2004,33(1):23-65
In this paper we determine the representation type of some algebras of infinite matrices continuously controlled at infinity by a compact metrizable space. We explicitly classify their finitely presented modules in the finite and tame cases. The algebra of row-column-finite (or locally finite) matrices over an arbitrary field is one of the algebras considered in this paper, its representation type is shown to be finite.Received October 2003 相似文献
2.
Philip Feinsilver 《Monatshefte für Mathematik》1987,104(2):89-108
Theq-analog and finite difference analog of the canonical Heisenberg-Weyl algebra are studied. The basic representations are found. Analogs of the standard boson Fock space are constructed. Various examples and illustrations are presented. 相似文献
3.
We consider a Poisson process ?? on an arbitrary measurable space with an arbitrary sigma-finite intensity measure. We establish an explicit Fock space representation of square integrable functions of ??. As a consequence we identify explicitly, in terms of iterated difference operators, the integrands in the Wiener?CIt? chaos expansion. We apply these results to extend well-known variance inequalities for homogeneous Poisson processes on the line to the general Poisson case. The Poincaré inequality is a special case. Further applications are covariance identities for Poisson processes on (strictly) ordered spaces and Harris?CFKG-inequalities for monotone functions of ??. 相似文献
4.
《随机分析与应用》2013,31(4):867-892
Abstract The main focus of the paper is a Clark–Ocone–Haussman formula for Lévy processes. First a difference operator is defined via the Fock space representation of L 2(P), then from this definition a Clark–Ocone–Haussman type formula is derived. We also derive some explicit chaos expansions for some common functionals. Later we prove that the difference operator defined via the Fock space representation and the difference operator defined by Picard [Picard, J. Formules de dualitésur l'espace de Poisson. Ann. Inst. Henri Poincaré 1996, 32 (4), 509–548] are equal. Finally, we give an example of how the Clark–Ocone–Haussman formula can be used to solve a hedging problem in a financial market modelled by a Lévy process. 相似文献
5.
Xiang Fang 《Geometric And Functional Analysis》2006,16(2):367-402
This paper concerns Fredholm theory in several variables, and its applications to Hilbert spaces of analytic functions. One
feature is the introduction of ideas from commutative algebra to operator theory. Specifically, we introduce a method to calculate
the Fredholm index of a pair of commuting operators. To achieve this, we define and study the Hilbert space analogs of Samuel
multiplicities in commutative algebra. Then the theory is applied to the symmetric Fock space. In particular, our results
imply a satisfactory answer to Arveson’s program on developing a Fredholm theory for pure d-contractions when d = 2, including both the Fredholmness problem and the calculation of indices. We also show that Arveson’s curvature invariant
is in fact always equal to the Samuel multiplicity for an arbitrary pure d-contraction with finite defect rank. It follows that the curvature is a similarity invariant.
Received: October 2004 Revision: May 2005 Accepted: May 2005
Partially supported by National Science Foundation Grant DMS 0400509. 相似文献
6.
We construct a representation of the infinite dimensional complex Clifford algebra on the Hilbert space of square-integrable
complex-valued functions on the Cantor set, which we show to be equivalent to the classical Fock representation. 相似文献
7.
I. V. Mikityuk 《Ukrainian Mathematical Journal》1990,42(4):472-477
We investigate Verma modules V over the generalized Virasoro current algebrag, which is the semidirect sum of the Virasoro algebra and the central extension of a commutative algebra. It is shown that an arbitrary unitary representation with highest weight of algebrag is isomorphic to the tensor product of a unitary Fock representation ofg (or of a one-dimensional representation ofg) and a unitary representation with highest weight of the Virasoro algebra (considered as a representation of algebrag). This result is used to obtain formulas for the determinants of the matrices defining the Shapovalov form on Verma module V.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 4, pp. 532–538, April, 1990. 相似文献
8.
Michael Anshelevich 《Proceedings of the American Mathematical Society》2008,136(7):2395-2405
Among all states on the algebra of non-commutative polynomials, we characterize the ones that have monic orthogonal polynomials. The characterizations involve recursion relations, Hankel-type determinants, and a representation as a joint distribution of operators on a Fock space.
9.
The rings of symmetric polynomials form an inverse system whose limit, the ring of symmetric functions, is the model for the bosonic Fock space representation of the affine Lie algebra. We show that this limit naturally carries an action of the affine Lie algebra (in the sense of Rouquier), thereby obtaining a family of categorifications of the bosonic Fock space representation. 相似文献
10.
Hiroyuki Chihara 《Integral Equations and Operator Theory》2009,63(3):321-335
We discuss the boundedness of Berezin-Toeplitz operators on a generalized Segal-Bargmann space (Fock space) over the complex
n-space. This space is characterized by the image of a global Bargmann-type transform introduced by Sj?strand. We also obtain
the deformation estimates of the composition of Berezin-Toeplitz operators whose symbols and their derivatives up to order
three are in the Wiener algebra of Sj?strand. Our method of proofs is based on the pseudodifferential calculus and the heat
flow determined by the phase function of the Bargmann transform.
Supported by the JSPS Grant-in-Aid for Scientific Research #20540151. 相似文献
11.
Let (E,Q) be a finite dimensional quadratic vector space over a finite field. For the natural representation -π of the isometry group G of (E,Q) in the space L 2(E) of all complex valued functions on E, we analyse when the intertwining algebra of π is generated by just one averaging operator. 相似文献
12.
《代数通讯》2013,41(9):3581-3608
Abstract We define generalized Virasoro operators acting on a Fock space V(Γ). These generalize the standard construction of Virasoro operators. By using the Jacobi Identity we compute the commutators of these operators. These operators result in an abelian extension of the toroidal Lie algebra. We explicitly describe the abelian extension. 相似文献
13.
A decomposition of the level-oneq-deformed Fock space representations ofU
q(sl
n
) is given. It is found that the action ofU
q(sl
n
) on these Fock spaces is centralized by a Heisenberg algebra, which arises from the center of the affine Hecke algebra
N in the limitN . Theq-deformed Fock space is shown to be isomorphic as aU
q(sl
n
)-Heisenberg-bimodule to the tensor product of a level-one irreducible highest weight representation ofU
q(sl
n
) and the Fock representation of the Heisenberg algebra. The isomorphism is used to decompose theq-wedging operators, which are intertwiners between theq-deformed Fock spaces, into constituents coming fromU
q(sl
n
) and from the Heisenberg algebra. 相似文献
14.
Michael Lau 《Advances in Mathematics》2005,194(2):225-245
Given any representation of an arbitrary Lie algebra g over a field K of characteristic 0, we construct representations of a central extension of g on bosonic and fermionic Fock space. The method gives an explicit formula for a (sometimes trivial) 2-cocycle in H2(g;K). We illustrate these techniques with several concrete examples. 相似文献
15.
Otto Kerner Andrzej Skowroński Kunio Yamagata Dan Zacharia 《Central European Journal of Mathematics》2004,2(1):103-111
The strong global dimension of a finite dimensional algebra A is the maximum of the width of indecomposable bounded differential complexes of finite dimensional projective A-modules. We prove that the strong global dimension of a finite dimensional radical square zero algebra A over an algebraically closed field is finite if and only if A is piecewise hereditary. Moreover, we discuss results concerning the finiteness of the strong global dimension of algebras
and the related problem on the density of the push-down functors associated to the canonical Galois coverings of the trivial
extensions of algebras by their repetitive algebras. 相似文献
16.
Rafał Bocian Thorsten Holm Andrzej Skowroński 《Central European Journal of Mathematics》2004,2(1):67-75
Auslander’s representation dimension measures how far a finite dimensional algebra is away from being of finite representation
type. In [1], M. Auslander proved that a finite dimensional algebra A is of finite representation type if and only if the representation dimension of A is at most 2. Recently, R. Rouquier proved that there are finite dimensional algebras of an arbitrarily large finite representation
dimension. One of the exciting open problems is to show that all finite dimensional algebras of tame representation type have
representation dimension at most 3. We prove that this is true for all domestic weakly symmetric algebras over algebraically
closed fields having simply connected Galois coverings. 相似文献
17.
Given a maximal rigid object T of the cluster tube, we determine the objects finitely presented by T. We then use the method of Keller and Reiten to show that the endomorphism algebra of T is Gorenstein and of finite representation type, as first shown by Vatne. This algebra turns out to be the Jacobian algebra of a certain quiver with potential, when the characteristic of the base field is not 3. We study how this quiver with potential changes when T is mutated. We also provide a derived equivalence classification for the endomorphism algebras of maximal rigid objects. 相似文献
18.
Anne V. Shepler 《Journal of Algebraic Combinatorics》2005,22(1):115-132
We consider generalized exponents of a finite reflection group acting on a real or complex vector space V. These integers are the degrees in which an irreducible representation of the group occurs in the coinvariant algebra. A basis for each isotypic component arises in a natural way from a basis of invariant generalized forms. We investigate twisted reflection representations (V tensor a linear character) using the theory of semi-invariant differential forms. Springer’s theory of regular numbers gives a formula when the group is generated by dim V reflections. Although our arguments are case-free, we also include explicit data and give a method (using differential operators) for computing semi-invariants and basic derivations. The data give bases for certain isotypic components of the coinvariant algebra. 相似文献
19.
Yun Gao 《Compositio Mathematica》2000,123(1):1-25
An irreducible representation of the extended affine Lie algebra of type A
n-1 coordinatized by a quantum torus of variables is constructed by using the Fock space for the principal vertex operator realization of the affine Lie algebra
. 相似文献
20.
Karl H. Hofmann Jimmie D. Lawson Wolfgang A. F. Ruppert 《Mathematische Nachrichten》1996,179(1):119-143
For each pair (??,??) consisting of a real Lie algebra ?? and a subalgebra a of some Cartan subalgebra ?? of ?? such that [??, ??]∪ [??, ??] we define a Weyl group W(??, ??) and show that it is finite. In particular, W(??, ??,) is finite for any Cartan subalgebra h. The proof involves the embedding of 0 into the Lie algebra of a complex algebraic linear Lie group to which the structure theory of Lie algebras and algebraic groups is applied. If G is a real connected Lie group with Lie algebra ??, the normalizer N(??, G) acts on the finite set Λ of roots of the complexification ??c with respect to hc, giving a representation π : N(??, G)→ S(Λ) into the symmetric group on the set Λ. We call the kernel of this map the Cartan subgroup C(??) of G with respect to h; the image is isomorphic to W(??, ??), and C(??)= {g G : Ad(g)(h)— h ε [h,h] for all h ε h }. All concepts introduced and discussed reduce in special situations to the familiar ones. The information on the finiteness of the Weyl groups is applied to show that under very general circumstance, for b ∪ ?? the set ??? ?(b) remains finite as ? ranges through the full group of inner automorphisms of ??. 相似文献