In mathematics, a vertex operator algebra (VOA) is an algebraic structure that plays an important role in two-dimensional conformal field theory and string...

of operators on a Hilbert space Vertex operator algebra – Algebra used in 2D conformal field theories and string theory Theory of Operator Algebras I By...

non-perturbative approach to quantum field theory. One example is the vertex operator algebra, which has been used to construct two-dimensional conformal field...

moonshine is now known to be underlain by a vertex operator algebra called the moonshine module (or monster vertex algebra) constructed by Igor Frenkel, James...

the vertex operator algebra. Affine Lie algebra Chiral model Jordan map Virasoro algebra Vertex operator algebra Kac–Moody algebra Goldin 2006 Kac, Victor...

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...

different Poisson algebra, one that would be much larger. For a vertex operator algebra (V, Y, ω, 1), the space V/C2(V) is a Poisson algebra with {a, b} =...

constructed from a given vertex operator algebra. Many important representation theoretic properties of the vertex algebra are logically related to properties...

a type of statistical mechanics model Vertex operator algebra in conformal field theory Media related to Vertex at Wikimedia Commons This disambiguation...

(1988). Vertex operator algebras and the Monster. Pure and Applied Mathematics. Vol. 134. Academic Press. ISBN 0-12-267065-5. Kac, Victor (1996). Vertex algebras...

structure. Vertex operator algebra Von Neumann algebra: a *-algebra of operators on a Hilbert space equipped with the weak operator topology. Algebraic structures...

Thompson group acts on a vertex operator algebra over the field with 3 elements. This vertex operator algebra contains the E8 Lie algebra over F3, giving the...

In algebraic and differential geometry, a Calabi–Yau manifold, also known as a Calabi–Yau space, is a particular type of manifold which has certain properties...

algebra Symmetric algebra Tensor algebra Universal enveloping algebra Vertex operator algebra von Neumann algebra Weyl algebra Zinbiel algebra This is a list...

representation over the field with 7 elements, and it acts naturally on a vertex operator algebra over the field with 7 elements. The smallest permutation representation...

Duncan (2006) used the 28-dimensional lattice to construct a vertex operator algebra acted on by the double cover. Alternatively, the double cover can...

2017-10-25. Frenkel, Igor; Lepowsky, James; Meurman, Arne (1988). Vertex Operator Algebras and the Monster. Pure and Applied Mathematics. Vol. 134. Academic...

naturally on a vertex operator algebra over the field with 5 elements (Lux, Noeske & Ryba 2008). This implies that it acts on a 133 dimensional algebra over F5...

a Kac–Moody algebra (named for Victor Kac and Robert Moody, who independently and simultaneously discovered them in 1968) is a Lie algebra, usually infinite-dimensional...

Lepowsky and Meurman, Vertex Operator Algebras and the Monster, Academic Press, 1988 ISBN 0-12-267065-5. Kac, Victor, Vertex Algebras for Beginners, Second...

Invent. Math. 79 (1985), 417-442. Stefano Capparelli, Vertex operator relations for affine algebras and combinatorial identities, Thesis (Ph.D.)–Rutgers...

Virasoro–Shapiro amplitude, the Virasoro algebra, the super Virasoro algebra, the Virasoro vertex operator algebra, the Virasoro group, the Virasoro conjecture...

of an affine Kac–Moody algebra at a fixed level can be encoded in a vertex algebra. The derivation d acts as the energy operator L0 on H0, which can be...

Virasoro algebra Mirror symmetry Conformal anomaly Conformal algebra Superconformal algebra Vertex operator algebra Loop algebra Kac–Moody algebra Wess–Zumino–Witten...

is given by the following data: Finite quiver Q {\displaystyle Q} Each vertex v ∈ V ⁡ ( Q ) {\displaystyle v\in \operatorname {V} (Q)} corresponds to...

group (or supergroup), and its symmetry algebra is the affine Lie algebra built from the corresponding Lie algebra (or Lie superalgebra). By extension, the...

anomaly Two-dimensional conformal field theory Vertex operator algebra W-algebra Virasoro algebra Lie algebra extension#Projective representation Group extension...

Virasoro algebra Mirror symmetry Conformal anomaly Conformal algebra Superconformal algebra Vertex operator algebra Loop algebra Kac–Moody algebra Wess–Zumino–Witten...

treatment of type IIA string theory belongs to symplectic topology and algebraic geometry, particularly Gromov–Witten invariants. At low energies, type...

Virasoro algebra Mirror symmetry Conformal anomaly Conformal algebra Superconformal algebra Vertex operator algebra Loop algebra Kac–Moody algebra Wess–Zumino–Witten...