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...
3 KB (348 words) - 05:59, 8 May 2025
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
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
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...
9 KB (875 words) - 15:22, 28 June 2025
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
Conformal geometry (section The conformal Lie algebras)
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
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...
794 bytes (63 words) - 17:45, 20 March 2022
enveloping algebra of a Lie algebra is the unital associative algebra whose representations correspond precisely to the representations of that Lie algebra. Universal...
51 KB (8,954 words) - 11:11, 9 February 2025
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...
5 KB (564 words) - 02:32, 4 June 2023
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...
4 KB (360 words) - 18:21, 28 June 2025
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...
10 KB (1,272 words) - 03:10, 7 July 2025
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...
33 KB (5,674 words) - 01:40, 21 January 2025
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....
2 KB (196 words) - 01:56, 25 May 2023
conformal symmetries of 2d Euclidean space is the infinite-dimensional Witt algebra. In 1908, Harry Bateman and Ebenezer Cunningham, two young researchers...
13 KB (1,935 words) - 11:07, 24 June 2025
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:...
62 KB (10,497 words) - 10:18, 26 June 2025
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...
9 KB (1,314 words) - 09:24, 3 April 2025
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...
21 KB (3,163 words) - 18:06, 2 May 2025
British Columbia in Vancouver, Canada. He completed his dissertation on Witt algebras in 1955. His thesis advisor was Stephen Arthur Jennings. Following the...
13 KB (1,387 words) - 18:57, 24 June 2025
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...
37 KB (7,686 words) - 15:36, 24 May 2025
Artin–Schreier theory (redirect from Artin–Schreier–Witt extension)
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...
3 KB (466 words) - 11:05, 28 May 2025
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...
6 KB (852 words) - 07:19, 17 June 2025
Ring (mathematics) (redirect from Ring (algebra))
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
Reductive group (redirect from Reductive algebraic group)
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