2002 Fiscal Year Final Research Report Summary
Subalgebras of lattice vertex operator algebras
| Project/Area Number |
13640012
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | Hitotsubashi University |
|---|
Principal Investigator |
YAMADA Hiromichi Hitotsubashi University, Graduate School of Economics, Professor, 大学院・経済学研究科, 教授 (50134888)
|
|---|
| Project Period (FY) |
2001 – 2002
|
| Keywords | vertex operator algebra / Virasoro algebra / conformal vector / highest weight vector / moonshine module / orbifold |
|---|
| Research Abstract |
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.
|
