姓名 陳憲揚 系所 應用數學系 職稱 助理教授 校內分機 588 EMAIL hychen@mail.nutn.edu.tw 辦公室 C504 網址 專長/研究領域 頂點算子代數 Vertex Operator Algebra

 著作名稱： Z3 -orbifold construction of the Moonshine vertex operator algebra and some maximal 3-local subgroups of the Monster 年度： 2017 類別： 期刊論文 摘要： Abstract In this article, we describe some maximal 3-local subgroups of the Monster simple group using vertex operator algebras (VOA). We first study the holomorphic vertex operator algebra obtained by applying the orbifold construction to the Leech lattice vertex operator algebra and a lift of a fixed-point free isometry of order 3 of the Leech lattice. We also consider some of its special subVOAs and study their stabilizer subgroups using the symmetries of the subVOAs. It turns out that these stabilizer subgroups are 3-local subgroups of its full automorphism group. As one of our main results, we show that its full automorphism group is isomorphic to the Monster simple group by using a 3-local characterization and that the holomorphic VOA is isomorphic to the Moonshine VOA. This approach allows us to obtain relatively explicit descriptions of two maximal 3-local subgroups of the shape 31+12 .2. Suz :2 and 38 . −(8, 3).2 in the Monster simple group. 關鍵字： 著作名稱： Quantum dimensions and fusion rules of the VOA $V^τ_{L_{C×D}}$, 年度： 2016 類別： 期刊論文 摘要： 關鍵字： vertex operator algebra, quantum dimension 著作名稱： Fusion rules among irreducible $V_{\sqrt {2}A_2}^\tau$-modules of twisted type, 年度： 2015 類別： 期刊論文 摘要： In this article, we first compute the quantum dimensions of irreducible Vτ√2A2 -modules. These quantum dimensions give upper bounds on fusion rules among irreducible Vτ√2A2 -modules. Together with the lower bounds obtained by Lam and the author, we determine explicitly fusion rules among all irreducible Vτ√2A2 -modules of twisted type. This work completes the program for determining the fusion rules among irreducible Vτ√2A2 -modules. 關鍵字： Fusion rules, Quantum dimension 著作名稱： Weyl groups and vertex operator algebras generated by Ising vectors satisfying (2B,3C) condition 年度： 2014 類別： 期刊論文 摘要： In this paper, we construct explicitly certain moonshine type vertex operator algebras generated by a set of Ising vectors I such that (1) for any e f ∈ I, the subVOA VOA(e, f ) generated by e and f is isomorphic to either U2B or U3C ; and (2) the subgroup generated by the corresponding Miyamoto involutions {τe | e ∈ I} is isomorphic to the Weyl group of a root system of type An , Dn , E6 , E7 or E8 . The structures of the corresponding vertex operator algebras and their Griess alge- bras are also studied. In particular, the central charge of these vertex operator algebras are determined. 關鍵字： Ising vectors, Weyl group 著作名稱： An explicit Majorana representation of the group$3^2{:}2$ of 3C-pure type 年度： 2014 類別： 期刊論文 摘要： We study a coset vertex operator algebra (VOA) W in the lattice VOA VE_^38. We show that the coset VOA W is generated by nine Ising vectors such that any two Ising vectors generate a 3C subVOA U3C , and the group generated by the corresponding Miyamoto involutions has shape 3^2 :2. This gives an explicit example for Majorana representations of the group 3^2 :2 of 3C-pure type. 關鍵字： Ising vectors, Majorana representation 著作名稱： Coset construction of $\mathbb{Z}/3$ orbifold vertex operator algebra $V^ \tau_{ \sqrt{2}A_2}$ 年度： 2013 類別： 期刊論文 摘要： In this paper, we give a coset construction of the orbifold VOA V√ τ , where τ is an 2A_2 order three automorphism of V√2A2 . The main idea is to use conjugations of several automorphisms of the lattice VOA VE6 , which in some sense are analogous to Frenkel–Lepowsky–Meurman’s triality map. As a consequence, we construct explicitly many intertwining operators among modules of twisted type and obtain lower bounds for their fusion rules. 關鍵字： vertex operator algebra, coset construction