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...

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...

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...

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...

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

(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...

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...

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

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...

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...

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

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

several closely related exceptional simple Lie groups, linear algebraic groups or Lie algebras of dimension 248; the same notation is used for the corresponding...

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...

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

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...

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

language of vertex operator algebras. There is a well-established theory that associates to every conformal field theory a vertex operator algebra. When this...

monster module, a vertex operator algebra, an infinite dimensional algebra containing the Griess algebra, and acts on the monster Lie algebra, a generalized...

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

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...

883-dimensional Griess algebra and the infinite-dimensional monster vertex operator algebra, and acts naturally on the monster Lie algebra. (Complete for orders...

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

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

related Hopf algebra which is the dual of the previous Hopf algebra. It can be identified with the Hopf algebra of graded differential operators at the origin...