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  2. Vertex operator algebra - Wikipedia

    en.wikipedia.org/wiki/Vertex_operator_algebra

    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.

  3. Monstrous moonshine - Wikipedia

    en.wikipedia.org/wiki/Monstrous_moonshine

    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 ...

  4. Lattice (order) - Wikipedia

    en.wikipedia.org/wiki/Lattice_(order)

    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).

  5. Complete lattice - Wikipedia

    en.wikipedia.org/wiki/Complete_lattice

    An example is the Knaster–Tarski theorem, which states that the set of fixed points of a monotone function on a complete lattice is again a complete lattice. This is easily seen to be a generalization of the above observation about the images of increasing and idempotent functions.

  6. Free lattice - Wikipedia

    en.wikipedia.org/wiki/Free_lattice

    The table shows an example computation to show that the words x∧z and x∧z∧(x∨y) denote the same value in every bounded lattice. The case of lattices that are not bounded is treated similarly, omitting rules 2. and 3. in the above construction. The solution of the word problem on free lattices has several interesting corollaries.

  7. Zhu algebra - Wikipedia

    en.wikipedia.org/wiki/Zhu_algebra

    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 ...

  8. Map of lattices - Wikipedia

    en.wikipedia.org/wiki/Map_of_lattices

    A residuated lattice is a lattice. (def) 15. A distributive lattice is modular. [3] 16. A modular complemented lattice is relatively complemented. [4] 17. A boolean algebra is relatively complemented. (1,15,16) 18. A relatively complemented lattice is a lattice. (def) 19. A heyting algebra is distributive. [5] 20. A totally ordered set is a ...

  9. Integrable system - Wikipedia

    en.wikipedia.org/wiki/Integrable_system

    The Belinski–Zakharov transform generates a Lax pair for the Einstein field equations; general solutions are termed gravitational solitons, of which the Schwarzschild metric, the Kerr metric and some gravitational wave solutions are examples. Exactly solvable statistical lattice models. 8-vertex model; Gaudin model; Ising model in 1- and 2 ...