TY - JOUR
AU - Shimakura, Hiroki
AB - In this article, we study the moonshine vertex operator algebra starting with the tensor product of three copies of the vertex operator algebra V2E8+, and describe it by the quadratic space over 𝔽2 associated to V2E8+. Using quadratic spaces and orthogonal groups, we show the transitivity of the automorphism group of the moonshine vertex operator algebra on the set of all full vertex operator subalgebras isomorphic to the tensor product of three copies of V2E8+, and determine the stabilizer of such a vertex operator subalgebra. Our approach is a vertex operator algebra analogue of ‘An E8‐approach to the Leech lattice and the Conway group’ by Lepowsky and Meurman. Moreover, we find new analogies among the moonshine vertex operator algebra, the Leech lattice and the extended binary Golay code.
TI - An E8‐approach to the moonshine vertex operator algebra
JO - Journal of the London Mathematical Society
DO - 10.1112/jlms/jdq078
DA - 2011-04-01
UR - https://www.deepdyve.com/lp/wiley/an-e8-approach-to-the-moonshine-vertex-operator-algebra-zTYInFLK3B
SP - 493
EP - 516
VL - 83
IS - 2
DP - DeepDyve
ER -