"Witt's theorem" or "the Witt theorem" may also refer to the Bourbaki–Witt fixed point theorem of order theory. In mathematics, Witt's theorem, named...

mathematics, the Bourbaki–Witt theorem in order theory, named after Nicolas Bourbaki and Ernst Witt, is a basic fixed-point theorem for partially ordered...

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

in 1991, shortly after his 80th birthday. Witt's work has been highly influential. His invention of the Witt vectors clarifies and generalizes the structure...

(quadratic forms) Witt's theorem (quadratic forms) Artin–Wedderburn theorem (abstract algebra) Artin–Zorn theorem (algebra) Brauer–Cartan–Hua theorem (ring theory)...

the free associative algebra generated by X. By the Poincaré–Birkhoff–Witt theorem it is the "same size" as the symmetric algebra of the free Lie algebra...

fixed-point theorem Banach fixed-point theorem Bekić's theorem Borel fixed-point theorem Bourbaki–Witt theorem Browder fixed-point theorem Brouwer fixed-point...

Poincaré-Bendixson theorem, on the existence of attractors for two-dimensional dynamical systems; Poincaré–Birkhoff–Witt theorem, concerning Lie algebras...

the enveloping algebra. Indeed, it follows from the Poincaré–Birkhoff–Witt theorem (discussed § below) that the elements 1 , e , e 2 , e 3 , … {\displaystyle...

the proofs of several theorems of crucial importance, for instance the Hahn–Banach theorem in functional analysis, the theorem that every vector space...

quadratic form Hasse–Minkowski theorem Quadric Ramanujan's ternary quadratic form Square class Witt group Witt's theorem A tradition going back to Gauss...

(Witt geometry) Witt group Witt index Witt polynomial Witt ring Grothendieck-Witt ring Witt scheme Witt's theorem Witt vector Witt vector cohomology...

{\displaystyle {\mathfrak {g}}} , then by the easy part of the Poincaré–Birkhoff–Witt theorem, we can rewrite Z Y α i 1 ⋯ Y α i M {\displaystyle ZY_{\alpha _{i_{1}}}\cdots...

{\displaystyle {\widetilde {C}}=C} . ◻ {\displaystyle \square } The Bourbaki–Witt theorem, together with the Axiom of choice, can be used to prove the Hausdorff...

Poincaré–Birkhoff–Witt theorem states that every Lie algebra embeds into the commutator Lie algebra of its universal enveloping algebra. Ado's theorem states that...

…) of ⊥ (see also the Kleene fixed-point theorem). Another fixed point theorem is the Bourbaki–Witt theorem, stating that if f {\displaystyle f} is a...

Séminaire Nicolas Bourbaki (1960–1969) Bourbaki–Witt theorem Bourbaki–Alaoglu theorem Jacobson–Bourbaki theorem Nikolaos Bourbakis, computer scientist A place...

described above, (1), as a Lie algebra of matrices. The Poincaré–Birkhoff–Witt theorem applies to determine the universal enveloping algebra U ( h n ) {\displaystyle...

Poincaré–Birkhoff–Witt theorem: an explicit description of the universal enveloping algebra of a Lie algebra. Poincaré–Bjerknes circulation theorem: theorem about...

filtration on the universal enveloping algebra and the Poincaré–Birkhoff–Witt theorem. Suppose that G is a group and K is a field. Is the group ring R = K[G]...

enveloping algebra of a Lie algebra is established by the Poincaré–Birkhoff–Witt theorem. Gröbner bases are also sometimes called standard bases. In physics,...

that it would also follow from the Schreier conjecture (see Witt (1998, p.277) for Witt's unpublished 1937 note about this), but the Schreier conjecture...

later given by Ernst Witt. Witt's proof is sketched below. Alternatively, the theorem is a consequence of the Skolem–Noether theorem by the following argument...

representation theorem Birkhoff's HSP theorem Birkhoff's theorem Birkhoff–Kakutani theorem Pierce–Birkhoff conjecture Pierce–Birkhoff ring Poincaré–Birkhoff–Witt theorem...

be used to perform the commutations required by the Poincaré–Birkhoff–Witt theorem used in the construction of a universal enveloping algebra. As such,...

F^{i+1}} using ⊆ as the ordering. So by a fixed-point theorem (specifically Bourbaki–Witt theorem), there exists a fixed point for this iterative process...

U({\mathfrak {g}})=T({\mathfrak {g}})/I} . It satisfies the Poincaré–Birkhoff–Witt theorem: if e 1 , … , e n {\displaystyle e_{1},\ldots ,e_{n}} is a basis for...

Birkhoff's theorem (disambiguation), multiple theorems Birkhoff decomposition, two different decompositions Birkhoff algorithm Poincaré–Birkhoff–Witt theorem This...

condition that the Poincaré–Birkhoff–Witt theorem holds (and, in general, they are necessary conditions for the theorem to hold). Just as for Lie algebras...

Law Field Person(s) Named After Abel's theorem Calculus Niels Henrik Abel Ariadne's thread Computer science Ariadne Amdahl's law Computer science Gene...