著作名稱：  Z3 orbifold construction of the Moonshine vertex operator algebra and some maximal 3local subgroups of the Monster 
年度：  2017 
類別：  期刊論文 
摘要：  Abstract In this article, we describe some maximal 3local 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 fixedpoint 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 3local 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 3local characterization and that the
holomorphic VOA is isomorphic to the Moonshine VOA. This approach allows us to obtain
relatively explicit descriptions of two maximal 3local 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 3Cpure 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 3Cpure
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 