W-algebras related to parafermion algebras |
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| Authors: | Chongying Dong Ching Hung Lam Hiromichi Yamada |
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| Affiliation: | aDepartment of Mathematics, University of California, Santa Cruz, CA 95064, USA;bDepartment of Mathematics and National Center for Theoretical Sciences, National Cheng Kung University, Tainan, Taiwan 701;cDepartment of Mathematics, Hitotsubashi University, Kunitachi, Tokyo 186-8601, Japan |
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| Abstract: | ![]()
We study a W-algebra of central charge 2(k−1)/(k+2), k=2,3,…, contained in the commutant of a Heisenberg algebra in a simple affine vertex operator algebra L(k,0) of type  with level k. We calculate the operator product expansions of the W-algebra. We also calculate some singular vectors in the case k 6 and determine the irreducible modules and Zhu's algebra. Furthermore, the rationality and the C2-cofiniteness are verified for such k. |
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| Keywords: | Vertex operator algebra W-algebra Parafermion algebra |
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