共查询到20条相似文献,搜索用时 62 毫秒
1.
Jianzhi Han 《Frontiers of Mathematics in China》2014,9(3):477-494
For any C2-cofinite vertex product and the P(z)-tensor product finite length are proved to exist, which operator superalgebra V, the tensor of any two admissible V-modules of are shown to be isomorphic, and their constructions are given explicitly in this paper. 相似文献
2.
Let V be a simple vertex operator algebra and G a finite automorphism group. Then there is a natural right G-action on the set of all inequivalent irreducible V-modules. Let be a finite set of inequivalent irreducible V-modules which is closed under the action of G. There is a finite dimensional semisimple associative algebra for a suitable 2-cocycle naturally determined by the G-action on such that and the vertex operator algebra form a dual pair on the sum of V-modules in in the sense of Howe. In particular, every irreducible V-module is completely reducible -module.
Received: 10 September, 2001 / Published online: 29 April 2002
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ID="*" Supported by NSF grants and a research grant from the Committee on Research, UC Santa Cruz.
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ID="**" Supported by DPST grant from government of Thailand. 相似文献
3.
Liang Kong 《Advances in Mathematics》2007,213(1):271-340
We study the operadic and categorical formulations of (conformal) full field algebras. In particular, we show that a grading-restricted R×R-graded full field algebra is equivalent to an algebra over a partial operad constructed from spheres with punctures and local coordinates. This result is generalized to conformal full field algebras over VL⊗VR, where VL and VR are two vertex operator algebras satisfying certain finiteness and reductivity conditions. We also study the geometry interpretation of conformal full field algebras over VL⊗VR equipped with a nondegenerate invariant bilinear form. By assuming slightly stronger conditions on VL and VR, we show that a conformal full field algebra over VL⊗VR equipped with a nondegenerate invariant bilinear form exactly corresponds to a commutative Frobenius algebra with a trivial twist in the category of VL⊗VR-modules. The so-called diagonal constructions [Y.-Z. Huang, L. Kong, Full field algebras, arXiv: math.QA/0511328] of conformal full field algebras are given in tensor-categorical language. 相似文献
4.
Let V be a vertex operator algebra and g =(1 2 ··· k) be a k-cycle which is viewed as an automorphism of the vertex operator algebra V?k. It is proved that Dong-Li-Mason’s associated associative algebra Ag(V?k) is isomorphic to Zhu’s algebra A(V) explicitly. This result recovers a previous result that there is a one-to-one correspondence between irreducible g-twisted V?k-modules and irreducible V-modules. 相似文献
5.
Edward Frenkel 《Advances in Mathematics》2004,187(1):195-227
We extend the geometric approach to vertex algebras developed by the first author to twisted modules, allowing us to treat orbifold models in conformal field theory. Let V be a vertex algebra, H a finite group of automorphisms of V, and C an algebraic curve such that H⊂Aut(C). We show that a suitable collection of twisted V-modules gives rise to a section of a certain sheaf on the quotient X=C/H. We introduce the notion of conformal blocks for twisted modules, and analyze them in the case of the Heisenberg and affine Kac-Moody vertex algebras. We also give a chiral algebra interpretation of twisted modules. 相似文献
6.
Toshiyuki Abe 《Mathematische Zeitschrift》2007,255(4):755-792
We give an example of an irrational C
2-cofinite vertex operator algebra whose central charge is −2d for any positive integer d. This vertex operator algebra is given as the even part of the vertex operator superalgebra generated by d pairs of symplectic fermions, and it is just the realization of the c = −2-triplet algebra given by Kausch in the case d = 1. We also classify irreducible modules for this vertex operator algebra and determine its automorphism group.
This research is supported in part by a grant from Japan Society for the Promotion of Science. 相似文献
7.
Tomoyuki Arakawa 《Mathematische Zeitschrift》2012,270(1-2):559-575
We show that a finitely strongly generated, non-negatively graded vertex algebra is C 2-cofinite if and only if it is lisse in the sense of Beilinson et al. (preprint). This shows that the C 2-cofiniteness is indeed a natural finiteness condition. 相似文献
8.
设 V 是一个顶点算子超代数. 该文得到了一系列的结合代数An(V)(对任何n∈ 1/2 + Z+(i∈ {0,1})). 也给出了An(V) -模但非An-1/2(V) -模的不可约模范畴和单的可容许的V -模的范畴之间的一一对应关系. 对于给定的An(V) -模但非An-1/2(V) -模U, 还构造了一类广义Verma可容许的V -模Mn(U). 进而利用结合代数的表示进一步研究了顶点算子超代数的表示论. 相似文献
9.
Teresa Conde 《Algebras and Representation Theory》2018,21(3):605-625
The ADR algebra R A of an Artin algebra A is a right ultra strongly quasihereditary algebra (RUSQ algebra). In this paper we study the Δ-filtrations of modules over RUSQ algebras and determine the projective covers of a certain class of R A -modules. As an application, we give a counterexample to a claim by Auslander–Platzeck–Todorov, concerning projective resolutions over the ADR algebra. 相似文献
10.
Qun-xing Pan 《代数通讯》2013,41(10):3955-3973
Let H be a Hopf algebra and A an H-bimodule algebra. This article investigates homological dimensions and Gorenstein dimensions of L-R smash products A?H. Several well-known results are generalized. Moreover, we explore the stability of Gorenstein projective (flat) precovers and Gorenstein injective preenvelopes between the category of left A-modules and the category of left A?H-modules. 相似文献
11.
This is the first part in a series of papers developing a tensor product theory for modules for a vertex operator algebra. The goal of this theory is to construct a vertex tensor category structure on the category of modules for a suitable vertex operator algebra. The notion of vertex tensor category is essentially a complex analogue of the notion of symmetric tensor category, and in fact a vertex tensor category produces a braided tensor category in a natural way. The theory applies in particular to many familiar rational vertex operator algebras, including those associated with WZNW models, minimal models and the moonshine module. In this paper (Part I), we introduce the notions ofP(z)- andQ(z)-tensor product, whereP(z) andQ(z) are two special elements of the moduli space of spheres with punctures and local coordinates, and we present the fundamental properties and constructions ofQ(z)-tensor products. 相似文献
12.
Ching Hung Lam 《代数通讯》2013,41(14):4339-4360
Given a commutative associative algebra A with an associative form (’), we construct a vertex operator algebra V with the weight two space V2;? A If in addition the form (’) is nondegenerate, we show that there is a simple vertex operator algebra with V2;? A We also show that if A is semisimple, then the vertex operator algebra constructed is the tensor products of a certain number of Virasoro vertex operator algebras. 相似文献
13.
The near-group rings are an important class of fusion rings in the theory of tensor categories. In this paper, the irreducible ?+-modules over the near-group fusion ring K(?3, 3) are explicitly classified. It turns out that there are only four inequivalent irreducible ?+-modules of rank 2 and two inequivalent irreducible ?+-modules of rank 4 over K(?3, 3). 相似文献
14.
For any module V over the two-dimensional non-abelian Lie algebra b and scalar α ∈ C, we define a class of weight modules F α (V) with zero central charge over the affine Lie algebra A 1 (1) . These weight modules have infinitedimensional weight spaces if and only if V is infinite dimensional. In this paper, we will determine necessary and sufficient conditions for these modules F α(V) to be irreducible. In this way, we obtain a lot of irreducible weight A 1 (1) -modules with infinite-dimensional weight spaces. 相似文献
15.
This paper mainly considers Toeplitz algebras, subnormal tuples and rigidity concerning reproducing C[z1,…,zd]-modules. By making use of Arveson's boundary representation theory, we find there is more rigidity in several variables than there is in single variable. We specialize our attention to reproducing C[z1,…,zd]-modules with -invariant kernels by examining the spectrum and the essential spectrum of the d-tuple {Mz1,…,Mzd}, and deducing an exact sequence of C∗-algebras associated with Toeplitz algebra. Finally, we deal with Toeplitz algebras defined on Arveson submodules and rigidity of Arveson submodules. 相似文献
16.
Fang Li 《Discrete Mathematics》2008,308(21):4978-4991
In this paper, we introduce the concept of a wide tensor category which is a special class of a tensor category initiated by the inverse braid monoids recently investigated by Easdown and Lavers [The Inverse Braid Monoid, Adv. in Math. 186 (2004) 438-455].The inverse braid monoidsIBn is an inverse monoid which behaves as the symmetric inverse semigroup so that the braid group Bn can be regarded as the braids acting in the symmetric group. In this paper, the structure of inverse braid monoids is explained by using the language of categories. A partial algebra category, which is a subcategory of the representative category of a bialgebra, is given as an example of wide tensor categories. In addition, some elementary properties of wide tensor categories are given. The main result is to show that for every strongly wide tensor category C, a strict wide tensor category Cstr can be constructed and is wide tensor equivalent to C with a wide tensor equivalence F.As a generalization of the universality property of the braid category B, we also illustrate a wide tensor category through the discussion on the universality of the inverse braid category IB (see Theorem 3.3, 3.6 and Proposition 3.7). 相似文献
17.
Bernhard Drabant 《Acta Appl Math》1996,44(1-2):117-132
We consider quasitriangular Hopf algebras in braided tensor categories introduced by Majid. It is known that a quasitriangular Hopf algebra H in a braided monoidal category C induces a braiding in a full monoidal subcategory of the category of H-modules in C. Within this subcategory, a braided version of the bosonization theorem with respect to the category C will be proved. An example of braided monoidal categories with quasitriangular structure deviating from the ordinary case of symmetric tensor categories of vector spaces is provided by certain braided supersymmetric tensor categories. Braided inhomogeneous quantum groups like the dilaton free q-Poincaré group are explicit applications.Supported in part by the Deutsche Forschungsgemeinschaft (DFG) through a research fellowship. 相似文献
18.
Brian Hartwig 《Linear algebra and its applications》2007,422(1):219-235
Recently Terwilliger and the present author found a presentation for the three-point sl2 loop algebra via generators and relations. To obtain this presentation we defined a Lie algebra ? by generators and relations and displayed an isomorphism from ? to the three-point sl2 loop algebra. In this paper we classify the finite-dimensional irreducible ?-modules. 相似文献
19.
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
20.
We study polynomial functors of degree 2, called quadratic, with values in the category of abelian groups Ab, and whose source category is an arbitrary category C with null object such that all objects are colimits of copies of a generating object E which is small and regular projective; this includes all categories of models V of a pointed theory T. More specifically, we are interested in such quadratic functors F from C to Ab which preserve filtered colimits and suitable coequalizers.A functorial equivalence is established between such functors F:C→Ab and certain minimal algebraic data which we call quadratic C-modules: these involve the values on E of the cross-effects of F and certain structure maps generalizing the second Hopf invariant and the Whitehead product.Applying this general result to the case where E is a cogroup these data take a particularly simple form. This application extends results of Baues and Pirashvili obtained for C being the category of groups or of modules over some ring; here quadratic C-modules are equivalent with abelian square groups or quadratic R-modules, respectively. 相似文献