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...

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...

algebra in two spacetime dimensions. The Virasoro algebra is the universal central extension of the Witt algebra. Central extensions are needed in physics, because...

Lie algebras, the Poincaré–Birkhoff–Witt theorem (or PBW theorem) is a result giving an explicit description of the universal enveloping algebra of a...

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...

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,...

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...

satisfying 1. and 2. Hence the Lie algebra of infinitesimal symmetries of the conformal structure, the Witt algebra, is infinite-dimensional. The conformal...

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...

Shirshov–Witt theorem Witt algebra Witt decomposition Witt design (Witt geometry) Witt group Witt index Witt polynomial Witt ring Grothendieck-Witt ring Witt scheme...

enveloping algebra of a Lie algebra is the unital associative algebra whose representations correspond precisely to the representations of that Lie algebra. Universal...

Witt algebra of infinitesimal conformal transformations has to be centrally extended. The quantum symmetry algebra is therefore the Virasoro algebra,...

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...

unification theory Supergroup Lie superalgebra Twistor theory Anyon Witt algebra Virasoro algebra Erlangen programme Homogeneous space Principal homogeneous space...

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...

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...

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...

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....

conformal symmetries of 2d Euclidean space is the infinite-dimensional Witt algebra. In 1908, Harry Bateman and Ebenezer Cunningham, two young researchers...

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:...

In mathematics, the exterior algebra or Grassmann algebra of a vector space V {\displaystyle V} is an associative algebra that contains V , {\displaystyle...

invariant. The technique can be further extended to the Witt algebra, which is the centerless Virasoro algebra. Spin wave Jordan–Wigner transformation Jordan–Schwinger...

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...

British Columbia in Vancouver, Canada. He completed his dissertation on Witt algebras in 1955. His thesis advisor was Stephen Arthur Jennings. Following the...

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...

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...

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...

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...

p-adic Theory in Noncommutative Algebras], Monatshefte für Mathematik (in German), 44 (1): 203–224, doi:10.1007/BF01699316 Witt, Ernst (1935), "Riemann-Rochscher...

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...