Haisheng Li
For a vertex operator algebra $V$, the regular representations are related to the $A_{n}(V)$-algebras and their bimodules, and induced $V$-modules from $A_{n}(V)$-modules are defined and studied in terms of the regular representations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
Tetramodule is a vector space supplied with the bimodule and bicomodule structures over a Hopf algebra. The exact definition is given. Some properties and applications to quantum groups are discussed.
Based on any chiral vertex operator algebra satisfying a suitable finiteness condition, the semisimplicity of the zero-mode algebra as well as a regularity for induced modules, we construct conformal field theory over the projective line with the chiral vertex operator algebra as symmetries of the theory. We appropriately generalize the argument in [TUY] so that we are able to define sheaves of conformal blocks for chiral vertex operator algebras and study them in detail. We prove the factorization theorem under the fairly general conditions for chiral vertex operator algebras and the zero-mod…
The solution of Deligne's conjecture on Hochschild cochains and the formality of the operad of little disks provide us with a natural homotopy Gerstenhaber algebra structure on the Hochschild cochains of an associative algebra. In this paper we construct a natural chain of quasi-isomorphisms of homotopy Gerstenhaber algebras between the Hochschild cochain complex C(A) of a regular commutative algebra A over a field of characteristic zero and the Gerstenhaber algebra of multiderivations of A. Unlike the original approach of the second author based on the computation of obstructions our method a…
We give an abstract construction, based on the Belavin-Polyakov-Zamolodchikov equations, of a family of vertex operator algebras of rank $26$ associated to the modified regular representations of the Virasoro algebra. The vertex operators are obtained from the tensor products of intertwining operators for a pair of Virasoro algebras. We explicitly determine the structure coefficients that yield the axioms of VOAs. In the process of our construction, we obtain new hypergeometric identities.
We give a natural extension of the notion of the contragredient module for a vertex operator algebra. By using this extension we prove that for regular vertex operator algebras, Zhu's $C_{2}$-finiteness condition holds, fusion rules are finite and the vertex operator algebras themselves are finitely generated.
We study Frobenius-Schur indicators of the regular representations of finite-dimensional semisimple Hopf algebras, especially group-theoretical ones. Those of various Hopf algebras are computed explicitly. In view of our computational results, we formulate the theorem of Frobenius for semisimple Hopf algebras and give some partial results on this problem.
We construct four families of Artin-Schelter regular algebras of global dimension four. Under some generic conditions, this is a complete list of Artin-Schelter regular algebras of global dimension four that are generated by two elements of degree 1. These algebras are also strongly noetherian, Auslander regular and Cohen-Macaulay. One of the main tools is Keller's higher-multiplication theorem on A-infinity Ext-algebras.
Twisted regular representations and bimodules in vertex operator algebra theory
本文利用顶点算子代数的扭状正则表示理论，构建扭状Zhu代数上的双模，扩展了Li在非扭情况下的工作，并证实了Dong和Jiang关于双模理论的猜想。
This survey paper contains a tutorial introduction to distance-regular graphs, with an emphasis on the subconstituent algebra and the $Q$-polynomial property.
We identify the algebra of matrix elements of big projective modules in category O with the regular functions on the big Bruhat cell of G. Analogous extensions of the regular representations of the affine Lie and Virasoro algebras yield vertex operator algebras, equipped with two commuting actions with special values of the total central charge. In the generic case, we identify the structure of these VOAs, compute their semi-infinite cohomology. Its superalgebra structure encodes the fusion rules for the associated tensor categories. Full details are provided for the affine sl(2) and Virasoro …
Let $A$ be a connected graded $k$-algebra with a balanced dualizing complex. We prove that $A$ is a Koszul AS-regular algebra if and only if that the Castelnuovo-Mumford regularity and the Ext-regularity coincide for all finitely generated $A$-modules. This can be viewed as a non-commutative version of \cite[Theorem 1.3]{ro}. By using Castelnuovo-Mumford regularity, we prove that any Koszul standard AS-Gorenstein algebra is AS-regular. As a preparation to prove the main result, we also prove the following statements are equivalent: (1) $A$ is AS-Gorenstein; (2) $A$ has finite left injective di…
Regular and higher regular graded algebras (in simplest case satisfying Von Neumann regularity $Θ_{1}Θ_{2}Θ_{1}=Θ_{1}$ instead of anticommutativity) are introduced and their properties are studied. They are described in terms of obstructed categories with nonclosed invertible and noninvertible morphisms for which generalized (obstructed) functors and natural transformations are given. Regular algebras and bialgebras are considered with examples. Corresponding regularizations of the cross product and Wick algebras are made.
Manin associated to a quadratic algebra (quantum space) the quantum matrix group of its automorphisms. This Talk aims to demonstrate that Manin's construction can be extended for quantum spaces which are non-quadratic homogeneous algebras. Here given a regular Artin-Schelter algebra of dimension 3 we construct the quantum group of its symmetries, i.e., the Hopf algebra of its automorphisms. For quadratic Artin-Schelter algebras these quantum groups are contained in the the classification of the GL(3) quantum matrix groups due to Ewen and Ogievetsky. For cubic Artin-Schelter algebras we obtain …
We first prove that for a Weyl algebra over a field of positive characteristic, its norm based extension is locally Auslander regular. We then prove that given an algebra which is Zariski locally isomorphic to the Weyl algebra, its norm based extension similarly defined is locally Auslander regular if and only if it is isomorphic to the original Weyl algebra.
The classification of affine prime regular Hopf algebras of GK-dimension one is completed. As consequences, 1) we give a negative answer to an open question posed by Brown-Zhang and 2) we show that there do exist prime regular Hopf algebras of GK-dimension one which are not pointed.
We study finite dimensional Hopf algebra actions on so-called filtered Artin-Schelter regular algebras of dimension n, particularly on those of dimension 2. The first Weyl algebra is an example of such on algebra with n=2, for instance. Results on the Gorenstein condition and on the global dimension of the corresponding fixed subrings are also provided.
This paper constitutes the first part of a program to classify all affine prime regular Hopf algebras $H$ of Gelfand-Kirillov dimension one over an algebraically closed field of characteristic zero. We prove a number of properties of such an algebra, list some classes of examples, and then prove that - when the PI-degree of $H$ is prime - our list contains all such algebras.
We prove a conjecture stated in a previous paper by the author about the existence of canonical filtrations for a family of vertex operator algebras in rational levels.
A regular vertex operator algebra is a vertex operator algebra such that any weak module (without grading) is a direct sum of ordinary irreducible modules. In this paper we give several sufficient conditions under which a rational vertex operator algebra is regular. We prove that the moonshine module vertex operator algebra $V^{\natural},$ the vertex operator algebras $L(l,0)$ associated with the integrable representations of affine algebras of level $l,$ the vertex operator algebras $L(c_{p,q},0)$ associated with irreducible highest weight representations for the discrete series of the Viraso…
Finite Gröbner-Shirshov bases for double extension regular algebras of type (14641)
本文用Matlab算法计算了(14641)型双重扩张正则代数的Gröbner-Shirshov基，并证明其具有PBW基。
Smooth geometry of double extension regular algebras of type (14641)
该研究针对(14641)型双扩张正则代数的几何性质展开，通过证明得出这类代数不具有微分光滑性的结论，为相关代数几何研究提供了结论支撑。
In this paper, quadratic algebras on which $\tilde{H}_4$, the Heisenberg group of order 64, acts as degree-preserving algebra automorphisms are studied. In particular, we show that if $\mathcal{A}$ is a four-dimensional Artin-Schelter regular quadratic $\tilde{H}_4$-algebra with the degree one part isomorphic to the Schrödinger representation of $\tilde{H}_4$, then $\mathcal{A}$ is (a twist of) a four-dimensional Sklyanin algebra or (a twist of) a quantum Clifford algebra of global dimension 4.
For every $m \in {\C} \setminus \{0, -2\}$ and every nonnegative integer $k$ we define the vertex operator (super)algebra $D_{m,k}$ having two generators and rank $ \frac{3 m}{m + 2}$. If $m$ is a positive integer then $D_{m,k}$ can be realized as a subalgebra of a lattice vertex algebra. In this case, we prove that $D_{m,k}$ is a regular vertex operator (super)algebra and find the number of inequivalent irreducible modules.
Some Artin-Schelter Regular Algebras From Dual Reflection Groups and their Geometry
本文提出对偶反射群概念作为Shephard-Todd-Chevalley定理的推广，给出阶为16的两个例子，并研究了三个相关四维Artin-Schelter正则代数的代数与几何性质。
We continue our study of the McKay Correspondence for grading preserving actions of semisimple Hopf algebras H on (noncommutative) Artin-Schelter regular algebras A. Here, we establish correspondences between module categories over A^H, over A\#H, and over \End_{A^H} A. We also study homological properties of (endomorphism rings of) maximal Cohen-Macaulay modules over A^H.
We prove a sharpened version of a conjecture of Dong-Mason about lattice subalgebras of a strongly regular vertex operator algebra $V$, and give some applications. These include the existence of a canonical conformal subVOA $W\otimes G\otimes Z \subseteq V$, and a generalization of the theory of minimal models.
In establishing a more general version of the McKay correspondence, we prove Auslander's theorem for actions of semisimple Hopf algebras H on noncommutative Artin-Schelter regular algebras A of global dimension two, where A is a graded H-module algebra, and the Hopf action on A is inner faithful with trivial homological determinant. We also show that each fixed ring A^H under such an action arises an analogue of a coordinate ring of a Kleinian singularity.
For any Koszul Artin-Schelter regular algebra A, we consider a version of the universal Hopf algebra aut(A) coacting on A, introduced by Manin. To study the representations (i.e. finite dimensional comodules) of this Hopf algebra, we use the Tannaka-Krein formalism. Specifically, we construct an explicit combinatorial rigid monoidal category U, equipped with a functor M to finite dimensional vector spaces such that aut(A)= coend_U(M). Using this pair (U,M) we show that aut(A) is quasi-hereditary as a coalgebra and in addition is derived equivalent to the representation category of U.
Actions of Drinfeld doubles of finite groups on Artin-Schelter regular algebras
本文研究有限群的Drinfeld双群在Artin-Schelter正则代数上的内忠实作用及其不变量代数，并对8阶和16阶四元数群给出显式计算结果。
We study polynomial Poisson algebras with some regularity conditions. Linear (Lie-Berezin-Kirillov) structures on dual spaces of semi-simple Lie algebras, quadratic Sklyanin elliptic algebras of \cite{FO1},\cite{FO2} as well as polynomial algebras recently described by Bondal-Dubrovin-Ugaglia (\cite{Bondal},\cite{Ug}) belong to this class. We establish some simple determinantal relations between the brackets and Casimirs in this algebras. These relations imply in particular that for Sklyanin elliptic algebras the sum of Casimir degrees coincides with the dimension of the algebra. We are discus…
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。