Algebra

# A Z 2-orbifold model of the symplectic fermionic vertex by Abe T.

By Abe T.

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Applied Algebra, Algebraic Algorithms and Error-Correcting Codes: 10th International Symposium,AAECC-10 San Juan de Puerto Rico, Puerto Rico, May 10–14, 1993 Proceedings

This quantity is the complaints of the tenth foreign Symposium on utilized Algebra, Algebraic Algorithms and Error-Correcting Codes (AAECC 10),held in Puerto Rico, may well 1993. the purpose of the AAECC conferences is to draw high-level learn papers and to inspire cross-fertilization between varied parts which percentage using algebraic equipment and methods for functions within the sciences of computing, communications, and engineering.

Additional resources for A Z 2-orbifold model of the symplectic fermionic vertex operator superalgebra

Example text

Therefore, we see that u ∈ SF[2d](0) . Hence M ⊂ SF[2d]. The SF + -module SF is decomposable. We see that the automorphism θ of A preserves ± the ideal A+ . Hence θ acts on SF. If we denote by SF the ±1-eigenspace of SF for ± + − + θ respectively, then SF are SF -modules and SF = SF ⊕ SF as SF + -modules. 2 The SF + -modules SF are reducible and indecomposable. ± Proof The SF + -modules SF are reducible because L0 does not act diagonally on ± ± them. 1, soc(SF ) = SF[2d] ∩ SF ∼ = SF ± respectively.

Rationality, regularity, and C2 -cofiniteness, Trans. Am. Math. Soc. 356 (8), 3391–3402 (2004) + 3. : Classification of irreducible modules for the vertex operator algebra VL ; general case. J. Algebra 273 (2), 657–685 (2004) 4. : A spanning set for VOA modules. J. Algebra 254, 125–151 (2002) 5. : Nonmeromorphic operator product expansion and C2 -cofiniteness for a family of W-algebras. J. Phys. A 39 (4), 951–966 (2006) 6. : Classification of irreducible modules for the vertex operator algebra M(1)+ .

Consequently, we see that W is isomorphic to either (SF + ) or (SF(θ )+ ). 15 For the vertex operator algebra SF + with d ≥ 2, any irreducible A(SF + )module is isomorphic to one in the list { (SF ± ), (SF(θ )± )}. Symplectic fermionic vertex operator superalgebra 787 5 Further structures of the vertex operator algebra SF + In this section we prove the irrationality of SF + by constructing reducible indecomposable SF + -modules, and determine the automorphism group of SF + . We also calculate the irreducible characters and their modular transformations.