Orbifolds of vertex operator algebras

研究了与正定偶格相关的顶点算子代数的自同构轨道，得到了以下结果。(1)对晶格顶点算子代数自同构的不可约扭模进行了分类。(2)研究了与A_2型根格√2相关的顶点算子代数。证明了具有一定3阶自同构的轨道具有3阶对称性。讨论了怪物的对称与3A元素的关系。(3)研究了一般秩为l的√2倍A_l型根格的顶点算子代数。在顶点算子代数内部构造了一个对偶子代数。(4)利用与√2型根格相关的顶点算子代数的3阶自同构，构造了一个中心电荷为6/5的W_3代数。对其不可约模块也进行了分类。(5)在一个与E_6型根格（√2）相关联的顶点算子代数中构造了一个顶点算子代数，物理学上称为三临界三态波茨模型。并对其不可约模块进行分类，确定融合规则。

Orbifolds by automorphisms of vertex operator algebras associated with positive definite even lattices were studied and the following results were obtained.(1)Irreducible twisted modules with respect to an automorphism of a lattice vertex operator algebra lifted from a fixed point free isometry of a lattice were classified.(2)A vertex operator algebra associated with √2 times a root lattice of type A_2 was studied. It was shown that the orbifold by a certain automorphism of order 3 possesses an order 3 symmetry. The relation of the symmetry and 3A elements of the monster was discussed.(3)A vertex operator algebra associated with √2 times a root lattice of type A_l for a general rank l was studied. A parafermion algebra was constructed inside the vertex operator algebra.(4)A W_3 algebra of central charge 6/5 was constructed inside an orbifold by an order 3 automorphism of a vertex operator algebra associated with √2 times a root lattice of type A_2. Its irreducible modules were classified also.(5)A vertex operator algebra, which is called a tricritical 3-state Potts model in physics, was constructed inside a vertex operator algebra associated with √2 times a root lattice of type E_6. Moreover, its irreducible modules were classified and the fusion rules were determined.