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...

Virasoro algebra (named after the physicist Miguel Ángel Virasoro) is a complex Lie algebra and the unique central extension of the Witt algebra. It is...

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...

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...

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

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

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

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...

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...

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,...

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

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

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...

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...

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...

a Witt algebra. By standard quantum-mechanical arguments, the symmetry algebra of conformal field theory must be the central extension of the Witt algebra...

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...

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:...

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...

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...

as the difference in the Witt ring of the ternary forms attached to the imaginary subspaces of A and B. The quaternion algebras are linked if and only if...

of Kansas. Her research involves commutative algebra, representation theory, and singularity theory. Witt is a 2005 graduate of the University of Chicago...

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...

every associative algebra can be turned into a Lie algebra. The anticommutator of two elements a and b of a ring or associative algebra is defined by {...

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...