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The construction of a lattice vertex operator algebra V L for an even lattice L of rank n. In physical terms, this is the chiral algebra for a bosonic string compactified on a torus R n / L . It can be described roughly as the tensor product of the group ring of L with the oscillator representation in n dimensions (which is itself isomorphic to ...
In mathematics, a vertex operator algebra (VOA) is an algebraic structure that plays an important role in two-dimensional conformal field theory and string theory. In addition to physical applications, vertex operator algebras have proven useful in purely mathematical contexts such as monstrous moonshine and the geometric Langlands correspondence.
The connections can partly be explained by thinking of the algebras as a tower of lattice vertex operator algebras. It just so happens that the vertex algebras at the bottom are so simple that they are isomorphic to familiar non-vertex algebras. Thus the connections can be seen simply as the consequence of some lattices being sub-lattices of ...
The quantum double model can be generalized to the case where the input data is given by a C* Hopf algebra. [7] In this case, the face and vertex operators are constructed using the comultiplication of Hopf algebra. For each vertex, the Haar integral of the input Hopf algebra is used to construct the vertex operator.
A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra.It consists of a partially ordered set in which every pair of elements has a unique supremum (also called a least upper bound or join) and a unique infimum (also called a greatest lower bound or meet).
The monster vertex algebra (or moonshine module) is a vertex algebra acted on by the monster group that was constructed by Igor Frenkel, James Lepowsky, and Arne Meurman. R. Borcherds used it to prove the monstrous moonshine conjectures, by applying the Goddard–Thorn theorem of string theory to construct the monster Lie algebra, an infinite-dimensional generalized Kac–Moody algebra acted ...
A vertex operator algebra is rational if the category of admissible modules is semisimple and there are only finitely many irreducibles. It was conjectured that rationality is equivalent to C 2 -cofiniteness and a stronger condition regularity, however this was disproved in 2007 by Adamovic and Milas who showed that the triplet vertex operator ...
In quantum field theory, the operator product expansion (OPE) is used as an axiom to define the product of fields as a sum over the same fields. [1] As an axiom, it offers a non-perturbative approach to quantum field theory. One example is the vertex operator algebra, which has been used to construct two-dimensional conformal field theories ...