Decompositions of the Moonshine Module with respect to subVOAs associated to codes over Z2k
نویسنده
چکیده
In this paper, we give decompositions of the moonshine module V ♮ with respect to subVOAs associated to extremal Type II codes over Z2k for an integer k ≥ 2. Those subVOAs are isomorphic to the tensor product of 24 copies of the charge conjugation orbifold VOA. Using such decompositions, we obtain some elements of type 4A (k odd) and 2B (k even) of the Monster simple group Aut(V ♮).
منابع مشابه
Decomposition of the Moonshine Module with respect to a code over Z2k
In this paper, we give a decomposition of the moonshine module V ♮ with respect to an extremal Type II code over Z2k for an integer k ≥ 2. Then we obtain automorphisms of V ♮, some 4A and 2B elements of the Monster with respect to the decomposition. We give examples of such a decomposition for some k and give the McKay-Thompson series for a 4A element.
متن کاملFramed vertex operator algebras, codes and the moonshine module
For a simple vertex operator algebra whose Virasoro element is a sum of commutative Virasoro elements of central charge 1 2 , two codes are introduced and studied. It is proved that such vertex operator algebras are rational. For lattice vertex operator algebras and related ones, decompositions into direct sums of irreducible modules for the product of the Virasoro algebras of central charge 1 ...
متن کاملLifts of automorphisms of vertex operator algebras in simple current extensions
In this article, we study isomorphisms between simple current extensions of a simple VOA. For example, we classify the isomorphism classes of simple current extensions of the VOAs V + √ 2E8 and V + Λ16 , where Λ16 is the Barnes-Wall lattice of rank 16. Moreover, we consider the same simple current extension and describe the normalizer of the abelian automorphism group associated with this exten...
متن کاملResults on Generalization of Burch’s Inequality and the Depth of Rees Algebra and Associated Graded Rings of an Ideal with Respect to a Cohen-Macaulay Module
Let be a local Cohen-Macaulay ring with infinite residue field, an Cohen - Macaulay module and an ideal of Consider and , respectively, the Rees Algebra and associated graded ring of , and denote by the analytic spread of Burch’s inequality says that and equality holds if is Cohen-Macaulay. Thus, in that case one can compute the depth of associated graded ring of as In this paper we ...
متن کاملGorenstein homological dimensions with respect to a semi-dualizing module over group rings
Let R be a commutative noetherian ring and Γ a finite group. In this paper,we study Gorenstein homological dimensions of modules with respect to a semi-dualizing module over the group ring . It is shown that Gorenstein homological dimensions of an -RΓ module M with respect to a semi-dualizing module, are equal over R and RΓ .
متن کامل