Vertex operator algebras and quantum group

2016 Fiscal Year Final Research Report

• Project/Area Number: 25400009
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: The University of Tokyo
• Principal Investigator: TSUCHIYA AKIHIRO 東京大学, カブリ数物連携宇宙研究機構, 上級科学研究員 (90022673)
• Project Period (FY): 2013-04-01 – 2017-03-31
• Keywords: 頂点作用素代数 / 共形場理論

Outline of Final Research Achievements

By using Lattice VOA of type A1 and Virasoro Screening operators, we defined extended W-algebra of A1-type. We use the Virasoro intertwining operators defined by iterative multi proceed of screening operators using nearly cycles of twisted de Rham theory of Selberg type. We analyzed the structure of abelian categories of modules of these extended W-algebras. These abelian categories have finite number of simple objects, and we could determine these structures. These results we published on international journal in 2015. Thereafter, we reconsidered these results and calculations. We define super symmetries extension of lattice VOA of A1 type. Furthermore, we analyzed the structures of this abelian categories of module of this super symmetric VOA. In other words, abelian category has finite number of simple objects and semi-simple as abelian categories.
We are now preparing the paper, and we would like to contribute in some international journals.

Free Research Field

数物系化学