• In mathematics, the complex Witt algebra, named after Ernst Witt, is the Lie algebra of meromorphic vector fields defined on the Riemann sphere that are...
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    mathematics, the Virasoro algebra is a complex Lie algebra and the unique nontrivial central extension of the Witt algebra. It is widely used in two-dimensional...
    23 KB (4,140 words) - 21:04, 24 May 2025
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    algebra in two spacetime dimensions. The Virasoro algebra is the universal central extension of the Witt algebra. Central extensions are needed in physics, because...
    99 KB (17,708 words) - 07:59, 9 April 2025
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    theorem is basic to the study of Lie algebras. In algebraic geometry, the Hasse–Witt matrix of an algebraic curve over a finite field determines the...
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  • Lie algebras, the Poincaré–Birkhoff–Witt theorem (or PBW theorem) is a result giving an explicit description of the universal enveloping algebra of a...
    14 KB (1,934 words) - 07:37, 10 June 2024
  • result giving a 1-cocycle for Vect(S1), the Lie algebra of smooth vector fields, and hence for the Witt algebra, the subalgebra of trigonometric polynomial...
    46 KB (7,170 words) - 00:44, 17 June 2025
  • Witt ring may be A ring of Witt vectors The Witt ring (forms), a ring structure on the Witt group of symmetric bilinear forms See also Witt algebra,...
    227 bytes (66 words) - 21:00, 30 December 2019
  • satisfying 1. and 2. Hence the Lie algebra of infinitesimal symmetries of the conformal structure, the Witt algebra, is infinite-dimensional. The conformal...
    21 KB (3,359 words) - 11:22, 10 January 2025
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    circle. Its Lie algebra is (more or less) the Witt algebra, whose central extension the Virasoro algebra (see Virasoro algebra from Witt algebra for a derivation...
    65 KB (9,490 words) - 15:29, 22 April 2025
  • Shirshov–Witt theorem Witt algebra Witt decomposition Witt design (Witt geometry) Witt group Witt index Witt polynomial Witt ring Grothendieck-Witt ring Witt scheme...
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  • enveloping algebra of a Lie algebra is the unital associative algebra whose representations correspond precisely to the representations of that Lie algebra. Universal...
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  • Witt algebra of infinitesimal conformal transformations has to be centrally extended. The quantum symmetry algebra is therefore the Virasoro algebra,...
    42 KB (7,035 words) - 18:33, 19 June 2025
  • theory. In mathematics, Witt's theorem, named after Ernst Witt, is a basic result in the algebraic theory of quadratic forms: any isometry between two subspaces...
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  • List of Lie groups topics (category Lie algebras)
    unification theory Supergroup Lie superalgebra Twistor theory Anyon Witt algebra Virasoro algebra Erlangen programme Homogeneous space Principal homogeneous space...
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  • and is essentially equivalent when K {\displaystyle K} is a field.) A Witt algebra is a differential ring that contains the field Q {\displaystyle \mathbb...
    61 KB (7,863 words) - 10:03, 30 June 2025
  • universal enveloping algebra of a free Lie algebra on a set X is the free associative algebra generated by X. By the Poincaré–Birkhoff–Witt theorem it is the...
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  • differential operators ℓ n {\displaystyle \ell _{n}} generate a Witt algebra. Unfortunately the Witt algebra on its own always generates a space of particle states...
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  • was the first to discover the central extension of the Witt algebra that gives the Virasoro algebra, though his discovery went unnoticed for many years....
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    conformal symmetries of 2d Euclidean space is the infinite-dimensional Witt algebra. In 1908, Harry Bateman and Ebenezer Cunningham, two young researchers...
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    algebra is the quotient ring U ( g ) = T ( g ) / I {\displaystyle U({\mathfrak {g}})=T({\mathfrak {g}})/I} . It satisfies the Poincaré–Birkhoff–Witt theorem:...
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    In mathematics, the exterior algebra or Grassmann algebra of a vector space V {\displaystyle V} is an associative algebra that contains V , {\displaystyle...
    77 KB (12,242 words) - 02:39, 1 July 2025
  • invariant. The technique can be further extended to the Witt algebra, which is the centerless Virasoro algebra. Spin wave Jordan–Wigner transformation Jordan–Schwinger...
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  • forms. The Witt ring of C, and indeed any algebraically closed field or quadratically closed field, is Z/2Z. The Witt ring of R is Z. The Witt ring of a...
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  • British Columbia in Vancouver, Canada. He completed his dissertation on Witt algebras in 1955. His thesis advisor was Stephen Arthur Jennings. Following the...
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  • mathematics, a Witt vector is an infinite sequence of elements of a commutative ring. Ernst Witt showed how to put a ring structure on the set of Witt vectors...
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  • Schreier (1927) introduced Artin–Schreier theory for extensions of prime degree p, and Witt (1936) generalized it to extensions of prime power degree pn. If K is a field...
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  • In mathematics, the Hasse–Witt matrix H of a non-singular algebraic curve C over a finite field F is the matrix of the Frobenius mapping (p-th power mapping...
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  • commutative ring A returns the ring Wn(A) of p-isotypic Witt vectors of length n over A. In algebraic topology, a ring spectrum is a spectrum X together with...
    99 KB (13,697 words) - 09:39, 16 June 2025
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    algebra. For example, Witt's decomposition theorem says that a nondegenerate quadratic form over a field is determined up to isomorphism by its Witt index...
    56 KB (8,018 words) - 09:30, 15 April 2025
  • Virasoro algebra A central extension of the Witt algebra of polynomial vector fields on a circle. w A complex number W A W-boson W-algebra A sort of...
    46 KB (5,167 words) - 07:55, 24 November 2024