Cyclic orbifolds of lattice vertex operator algebras having group-like fusions
Let L be an even (positive definite) lattice and g ∈ O ( L ) . In this article, we prove that the orbifold vertex operator algebra V L g ^ has group-like fusion if and only if g acts trivially on the discriminant group D ( L ) = L ∗ / L (or equivalently ( 1 - g ) L ∗ < L ). We also determine thei...
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| Published in | Letters in mathematical physics Vol. 110; no. 5; pp. 1081 - 1112 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Dordrecht
Springer Netherlands
01.05.2020
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0377-9017 1573-0530 |
| DOI | 10.1007/s11005-019-01251-2 |
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| Abstract | Let
L
be an even (positive definite) lattice and
g
∈
O
(
L
)
. In this article, we prove that the orbifold vertex operator algebra
V
L
g
^
has group-like fusion if and only if
g
acts trivially on the discriminant group
D
(
L
)
=
L
∗
/
L
(or equivalently
(
1
-
g
)
L
∗
<
L
). We also determine their fusion rings and the corresponding quadratic space structures when
g
is fixed point free on
L
. By applying our method to some coinvariant sublattices of the Leech lattice
Λ
, we prove a conjecture proposed by G. Höhn. In addition, we also discuss a construction of certain holomorphic vertex operator algebras of central charge 24 using the orbifold vertex operator algebra
V
Λ
g
g
^
. |
|---|---|
| AbstractList | Let L be an even (positive definite) lattice and g∈O(L). In this article, we prove that the orbifold vertex operator algebra VLg^ has group-like fusion if and only if g acts trivially on the discriminant group D(L)=L∗/L (or equivalently (1-g)L∗<L). We also determine their fusion rings and the corresponding quadratic space structures when g is fixed point free on L. By applying our method to some coinvariant sublattices of the Leech lattice Λ, we prove a conjecture proposed by G. Höhn. In addition, we also discuss a construction of certain holomorphic vertex operator algebras of central charge 24 using the orbifold vertex operator algebra VΛgg^. Let L be an even (positive definite) lattice and g ∈ O ( L ) . In this article, we prove that the orbifold vertex operator algebra V L g ^ has group-like fusion if and only if g acts trivially on the discriminant group D ( L ) = L ∗ / L (or equivalently ( 1 - g ) L ∗ < L ). We also determine their fusion rings and the corresponding quadratic space structures when g is fixed point free on L . By applying our method to some coinvariant sublattices of the Leech lattice Λ , we prove a conjecture proposed by G. Höhn. In addition, we also discuss a construction of certain holomorphic vertex operator algebras of central charge 24 using the orbifold vertex operator algebra V Λ g g ^ . |
| Author | Lam, Ching Hung |
| Author_xml | – sequence: 1 givenname: Ching Hung orcidid: 0000-0002-7583-1031 surname: Lam fullname: Lam, Ching Hung email: chlam@math.sinica.edu.tw organization: Institute of Mathematics, Academia Sinica |
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| Keywords | Cyclic orbifold Group-like fusion Secondary 11H56 Primary 17B69 Vertex operator algebra Leech lattice |
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| Snippet | Let
L
be an even (positive definite) lattice and
g
∈
O
(
L
)
. In this article, we prove that the orbifold vertex operator algebra
V
L
g
^
has group-like... Let L be an even (positive definite) lattice and g∈O(L). In this article, we prove that the orbifold vertex operator algebra VLg^ has group-like fusion if and... |
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| SubjectTerms | Algebra Complex Systems Geometry Group Theory and Generalizations Lattices (mathematics) Mathematical analysis Mathematical and Computational Physics Physics Physics and Astronomy Subgroups Theoretical |
| Title | Cyclic orbifolds of lattice vertex operator algebras having group-like fusions |
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