現代教養学部

山内 博

ヤマウチ ヒロシ  (Hiroshi Yamauchi)

基本情報

所属
東京女子大学 現代教養学部 数理科学科 教授
学位
理学(博士)(筑波大学)

研究者番号
40452213
J-GLOBAL ID
201801006583250090
researchmap会員ID
B000326093

数学・代数学・頂点作用素代数
Mathematics/Algebra/Vertex operator algebras

研究キーワード

 2

論文

 26
  • Ching Hung Lam, Hiroshi Yamauchi
    Transactions of the American Mathematical Society 375(3) 2025-2067 2022年1月7日  
    <p>In this paper, we present a general construction of 3-transposition groups as automorphism groups of vertex operator algebras. Applying to the moonshine vertex operator algebra, we establish the Conway-Miyamoto correspondences between Fischer 3-transposition groups and and and Virasoro vectors of subalgebras of the moonshine vertex operator algebra.</p>
  • Hiromichi Yamada, Hiroshi Yamauchi
    Journal of Algebra 573 451-475 2021年5月  
  • Tomoyuki ARAKAWA, Hiromichi YAMADA, Hiroshi YAMAUCHI
    Journal of the Mathematical Society of Japan 73(1) 185-209 2021年1月  
  • Hiromichi Yamada, Hiroshi Yamauchi
    2018年4月23日  
    We study simple current extensions of tensor products of two vertex operator<br /> algebras satisfying certain conditions. We establish the relationship between<br /> the fusion rule for the simple current extension and the fusion rule for a<br /> tensor factor. In some special case, we construct a chain of simple current<br /> extensions. As an example, we obtain a chain of simple current extensions<br /> starting from the simple affine vertex operator algebra associated with<br /> $\widehat{sl}_2$ at level a positive integer $k$. The irreducible modules are<br /> classified and the fusion rules are determined for those simple current<br /> extensions.
  • Cuipo Jiang, Ching Hung Lam, Hiroshi Yamauchi
    Mathematische Zeitschrift 2018年  査読有り
    We prove the uniqueness of the simple vertex operator algebra of OZ-type<br /> generated by Ising vectors of $\sigma$-type. We also prove that the simplicity<br /> can be omitted if the Griess algebra is isomorphic to the Matsuo algebra<br /> associated with the root system of type $A_n$.

MISC

 1
  • Hiroshi Yamauchi
    2002年3月9日  
    We investigate a general theory of the Z_2-twisted representations of vertex<br /> operator superalgebras. Certain one-to-one correspondence theorems are<br /> established. We also give an explicit realization of the Ising model SVOA and<br /> its Z_2-twisted modules. As an application, we obtain the Gerald Hoehn&#039;s<br /> Babymonster SVOA VB and its Z_2-twisted module VB_{tw} from the moonshine VOA<br /> V^\nat by cutting off the Ising models. It is also shown in this paper that Aut<br /> (VB) is finite.

共同研究・競争的資金等の研究課題

 11