Subalgebras of lattice vertex operator algebras

研究了A、D、E型普通根格的√&lt；2&gt；格L的顶点算子代数的结构。2001年，研究了格点算子代数分解为由相互正交的共形向量生成的子代数的不可约模的直和问题。在L=√&lt；2a&gt；_1的情况下，确定了所有至多2个权的最高权向量。在L=√&lt；2D&gt；_1的情形下，对于一定的共形向量的选择，确定了所有最高权向量。利用L=√&lt；2a&gt；_3情形，利用Z_8码构造了一类新型的顶点算子代数。得到了与L=√&lt；2a&gt；_3情形相关的点算子代数模的月亮模的完全分解，并在2002年研究了3阶自同构的orbilold。中心电荷为6/5的W_3代数是√&lt；2a&gt；_2型格点算子代数的一个子代数。

The structure of vertex operator algebra associated with a lattice L which is √<2> times an ordinary root lattice of type A, D, or E was studied. In 2001, the decomposition of the lattice vertex operator algebra into a direct sum of irreducible modules for a subalgebra generated by mutually orthogonal conformal vectors was studied.1. In the case L = √<2A>_1, all highest weight vectors of weight at most 2 are determined.2. In the case L= √<2D>_1, all highest weight vectors are determined for a certain choice of conformal vectors.3. Using the case L = √<2A>_3, a new type of vertex operator algebras are constructed from Z_8 codes.4. A complete decomposition of the moonshine module as a module for a certain vertex operator algebra related to the case L = √<2A>_3 is obtained.In 2002, the orbifold for an automorphism of order 3 was studied.5. The W_3 algebra of central charge 6/5 is discovered as a subalgebra of the orbifold of the lattice vertex operator algebra of type √<2A>_2.