Bulg. J. Phys. vol.35 no.s1 (2008), pp. 25- 35

W-Algebras in Lattice Vertex Operator Algebras

Chongying Dong1, Ching Hung Lam2, Hiromichi Yamada3
1Department of Mathematics, University of California, Santa Cruz, CA 95064
2Department of Mathematics, National Cheng Kung University, Tainan, Taiwan 701
3Department of Mathematics, Hitotsubashi University, Kunitachi, Tokyo 186-8601, Japan
Abstract. We study a W-algebra of central charge 2(l-1)/(l+2), l = 2, 3, ..., which is the commutant of a Virasoro algebra of central charge 1 in the simple affine vertex operator algebra L(l,0) of type A1(1) with level l. The irreducible modules and Zhu's algebra are determined for l ≤ 6.

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