Rationality of the vertex algebra V + L when L is a nondegenerate even lattice of arbitrary rank
نویسنده
چکیده
In this paper we prove that the vertex algebra V + L is rational if L is a negative definite even lattice of finite rank , or if L is a non-degenerate even lattice of a finite rank that is neither positive definite nor negative definite. In particular, for such even lattices L, we show that the Zhu algebras of the vertex algebras V + L are semisimple. This extends the result of Abe from [A2] which establishes the rationality of V + L when L is a positive definite even lattice of finite rank.
منابع مشابه
When L Is a Rank One Lattice
Let L be a rank one positive definite even lattice. We prove that the vertex operator algebra (VOA) V + L satisfies the C2 condition. Here, V + L is the fixed point sub-VOA of the VOA VL associated with the automorphism lifted from the -1 isometry of L.
متن کاملRationality of vertex operator algebras
It is shown that a simple vertex operator algebra V is rational if and only if its Zhu algebra A(V ) is semisimple and each irreducible admissible V -module is ordinary. A contravariant form on a Verma type admissible V -module is constructed and the radical is exactly the maximal proper submodule. As an application the rationality of V + L for any positive definite even lattice is obtained.
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The automorphism group of the vertex operator algebra V + L is studied by using its action on isomorphism classes of irreducible V + L -modules. In particular, the shape of the automorphism group of V + L is determined when L is isomorphic to an even unimodular lattice without roots, √ 2R for an irreducible root lattice R of type ADE and the Barnes-Wall lattice of rank 16.
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We believe that the study of the notions of universal algebra modelled in an arbitarry topos rather than in the category of sets provides a deeper understanding of the real features of the algebraic notions. [2], [3], [4], [S], [6], [7], [13], [14] are some examples of this approach. The lattice Id(L) of ideals of a lattice L (in the category of sets) is an important ingredient of the categ...
متن کاملct 2 00 2 Classification of irreducible modules for the vertex operator algebra V + L : General case
The irreducible modules for the fixed point vertex operator subalgebra V + L of the vertex operator algebra VL associated to an arbitrary positive definite even lattice L under the automorphism lifted from the −1 isometry of L are classified.
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تاریخ انتشار 2008