The structure of parafermion vertex operator algebras: general case
نویسندگان
چکیده
The structure of the parafermion vertex operator algebra associated to an integrable highest weight module for any affine Kac-Moody algebra is studied. In particular, a set of generators for this algebra has been determined.
منابع مشابه
The Structure of Parafermion Vertex Operator Algebras
It is proved that the parafermion vertex operator algebra associated to the irreducible highest weight module for the affine Kac-Moody algebra A (1) 1 of level k coincides with a certain W -algebra. In particular, a set of generators for the parafermion vertex operator algebra is determined.
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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 A (1) 1 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,...
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It is proved that for a vector space W , any set of parafermion-like vertex operators on W in a certain canonical way generates a generalized vertex algebra in the sense of [DL2] with W as a natural module. This result generalizes a result of [Li2]. As an application, generalized vertex algebras are constructed from Lepowsky-Wilson’s Z-algebras of any nonzero level.
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I discuss a realization of stress-tensor for parafermion theories following the generalized Frenkel-Kac construction for higher level Kac-Moody algebras. All the fields are obtained from d=rank free bosons compactified on torus. This gives an alternative realization of Virasoro algebra in terms of a non-local correction of a free field construction which does not fit the usual background charge...
متن کاملLocal and Semilocal Vertex Operator Algebras
We initiate a general structure theory for vertex operator algebras V . We discuss the center and the blocks of V , the Jacobson radical and solvable radical, and local vertex operator algebras. The main consequence of our structure theory is that if V satisfies some mild conditions, then it is necessarily semilocal, i.e. a direct sum of local vertex operator algebras.
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تاریخ انتشار 2009