| Project/Area Number |
15540015
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Hitotsubashi University |
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Principal Investigator |
YAMADA Hiromichi Hitotsubashi University, Graduate School of Economics, Professor, 大学院・経済学研究科, 教授 (50134888)
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| Project Period (FY) |
2003 – 2004
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| Project Status |
Completed (Fiscal Year 2004)
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| Budget Amount *help |
¥2,200,000 (Direct Cost: ¥2,200,000)
Fiscal Year 2004: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2003: ¥1,200,000 (Direct Cost: ¥1,200,000)
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| Keywords | vertex operator algebra / orbifold / Virasoro algebra / fusion rule / parafermion algebra / W algebra / ムーンシャイン加群 |
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| Research Abstract |
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.
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