Search results
Results From The WOW.Com Content Network
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 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 ...
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).
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 ...
Stabilizer operators are defined on the spins around each vertex and plaquette [definition needed] (or face i.e. a vertex of the dual lattice) [clarification needed] of the lattice as follows, A v = ∏ i ∈ v σ i x , B p = ∏ i ∈ p σ i z . {\displaystyle A_{v}=\prod _{i\in v}\sigma _{i}^{x},\,\,B_{p}=\prod _{i\in p}\sigma _{i}^{z}.}
The A n root lattice – that is, the lattice generated by the A n roots – is most easily described as the set of integer vectors in R n+1 whose components sum to zero. The A 2 root lattice is the vertex arrangement of the triangular tiling .
In geometry and group theory, a lattice in the real coordinate space is an infinite set of points in this space with the properties that coordinate-wise addition or subtraction of two points in the lattice produces another lattice point, that the lattice points are all separated by some minimum distance, and that every point in the space is within some maximum distance of a lattice point.
Let X be a topological space, Y a Banach lattice and 𝒞(X,Y) the space of continuous bounded functions from X to Y with norm ‖ ‖ = ‖ ‖. Then 𝒞( X , Y ) is a Banach lattice under the pointwise partial order: f ≤ g ⇔ ( ∀ x ∈ X ) ( f ( x ) ≤ g ( x ) ) . {\displaystyle {f\leq g}\Leftrightarrow (\forall x\in X)(f(x)\leq g(x ...