相关论文: Vertex algebras and elliptic genera

We give a corrected version of Corollary 3.33 in: H. Flenner, S. Kaliman, and M. Zaidenberg, Birational transformations of weighted graphs. Affine algebraic geometry. Osaka Univ. Press, 2007, 107-147.

We first provide an overview of several results dealing with the genus of a division algebra and highlight the role of ramification in its analysis. We then give a survey of recent developments on the genus problem for simple algebraic…

We introduce a family of unital associative algebras A which are multiparameter analogues of the Weyl algebras and determine the simple weight modules and the Whittaker modules for them. All these modules can be regarded as spaces of…

This article contains: - Proofs of certain results recently obtained by D. Panyushev. - An addendum to the "inequality of Panyushev". - Calculations of indexes of certain contracted Lie algebras. - Examples of additivity of the index of Lie…

These are notes for a mini-course of 3 lectures given at the St. Petersburg School in Probability and Statistical Physics (June 2012). My aim was to explain, on the example of a particular model, how ideas from the representation theory of…

This paper constructs a presentation for the orthogonal groups. The amalgam is contained in that constructed by Ralf Gramlich Hendrik Van Maldeghem and arXiv:0708.1583 but it's shorter.

This is a survey talk on the study of Gel'fand-Dorfman bialgebras.

A slightly extended version, with a footnote added on December 19, 1997, of a contributed Abstract to the Eight Marcel Grossmann Meeting, Jerusalem, June 1997.

We construct a genus one analogue of the theory of associators and the Grothendieck-Teichmueller group. The analogue of the Galois action on the profinite braid groups is an action of the arithmetic fundamental group of a moduli space of…

This paper, together with a forthcoming paper by the author and Seitz, proves the Margulis-Platonov conjecture concerning the normal subgroup structure of algebraic groups over number fields, in the case of inner forms of anisotropic groups…

This book is expository and is in Russian. It is shown how in the course of solution of interesting geometric problems (close to applications) naturally appear main notions of algebraic topology (homology groups, obstructions and…

Survey written for the Proceedings of the AMS Meeting on Algebraic Geometry, Seattle, 2005. Based on the talk delivered at this occasion, but a few comments on recent developments are added.

We prove a Meyers type regularity estimate for approximate solutions of second order elliptic equations obtained by Galerkin methods. The proofs rely on interpolation results for Sobolev spaces on graphs. Estimates for second order elliptic…

In this note, the correction to the proof of one theorem in some our previous paper [arXiv:1302.0589] will be given.

The paper gives topological as well as rigid isotopy classification of smooth irreducible algebraic curves in the real projective 3-space for the case when the degree of the curve is at most six and its genus is at most one.

This article was originally published in Topology 22 (1983). The present hyperTeXed redaction includes references to post-1983 results as Addenda, and corrects a few typographical errors. (See math.GT/0411115 for a more comprehensive…

In this note we show how to apply the Gr\"obner--Shirshov bases (GSB) method for modules over an associative algebra to the study of vertex algebras defined by generators and relations. We compute GSBs for a series of vertex algebras and…

We consider the extension of the Heisenberg vertex operator algebra by all its irreducible modules. We give an elementary construction for the intertwining vertex operators and show that they satisfy a complex parametrized generalized…

These notes are an introduction to symplectic groupoids and the double structures associated with them. The treatment is intended to lie about midway between the original account of Coste, Dazord and Weinstein, which relied on effective use…

This is an unchanged version of an unpublished, ``state of the art'' survey given at a conference held in Stuttgart in 2001 to celebrate the 100th birthday of Richard Brauer. This text was recently quoted in several papers on the…