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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Lie algebras, the Poincaré–Birkhoff–Witt theorem (or PBW theorem) is a result giving an explicit description of the universal enveloping algebra of a...
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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...
35 KB (7,389 words) - 06:45, 24 August 2023
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...
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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...
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(linguist and mathematician) Superspace Exterior algebra DeWitt 1984, Chapter 1, page 1. DeWitt 1984, pp. 1–2. DeWitt 1984, p. 2. Rogers 2007a, Chapter 1 (available...
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DeWitt Clinton High School is a public high school located since 1929 in The Bronx, New York. Opened in 1897 in Lower Manhattan as an all-boys school,...
67 KB (6,775 words) - 15:38, 6 September 2024
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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Multivariate Statistics. Academic Press. pp. 455–464. ISBN 0-12-398750-4. DeWitt, Bryce (1984). "Chapter 1". Supermanifolds. Cambridge University Press....
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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...
55 KB (7,845 words) - 18:28, 24 April 2024
Crystalline cohomology (redirect from Algebraic de Rham theorem)
X over a base field k. Its values Hn(X/W) are modules over the ring W of Witt vectors over k. It was introduced by Alexander Grothendieck (1966, 1968)...
15 KB (1,922 words) - 09:44, 26 September 2022
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...
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Commutator (category Abstract algebra)
x^{y}\right]=1.} Identity (5) is also known as the Hall–Witt identity, after Philip Hall and Ernst Witt. It is a group-theoretic analogue of the Jacobi identity...
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Luc Illusie (category Algebraic geometers)
cotangent complex and deformations, crystalline cohomology and the De Rham–Witt complex, and logarithmic geometry. In 2012, he was awarded the Émile Picard...
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1987 – "Witt rings as integral rings", Invent. Math. 90, no. 3, 631–633. 1985 – "Periodicity of Clifford algebras and exact octagons of Witt groups",...
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Alexander Grothendieck (category CS1 German-language sources (de))
for schemes over a base field, whose values are modules over the ring of Witt vectors over the base field, that replaces Zariski open sets by infinitesimal...
77 KB (8,340 words) - 18:04, 9 September 2024
Kähler differential (redirect from Algebraic de Rham cohomology)
differential graded algebra is isomorphic to the derived de-Rham complex. The de Rham–Witt complex is, in very rough terms, an enhancement of the de Rham complex...
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In mathematics, Witt vector cohomology was an early p-adic cohomology theory for algebraic varieties introduced by Serre (1958). Serre constructed it by...
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L-theory (redirect from Algebraic L-group)
even-dimensional L-groups L 2 k ( R ) {\displaystyle L_{2k}(R)} are defined as the Witt groups of ε-quadratic forms over the ring R with ϵ = ( − 1 ) k {\displaystyle...
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Field (mathematics) (redirect from Field (algebra))
a fixed field F is isomorphic to the set of ring homomorphisms from the Witt ring W(F) of quadratic forms over F, to Z. An Archimedean field is an ordered...
87 KB (10,299 words) - 05:26, 5 September 2024
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 (13,632 words) - 06:07, 27 August 2024
Jean-Pierre Serre (category Academic staff of the Collège de France)
1954–55 was one based on Witt vector coefficients. Around 1958 Serre suggested that isotrivial principal bundles on algebraic varieties – those that become...
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has a fixed point, and indeed a smallest fixed point. See also Bourbaki–Witt theorem. The theorem has applications in abstract interpretation, a form...
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Group scheme (category Algebraic groups)
with coefficients in Witt vectors of k. F and V are the Frobenius and Verschiebung operators, and they may act nontrivially on the Witt vectors. Dieudonne...
20 KB (2,860 words) - 07:46, 11 February 2024
Emmy Noether (category CS1 German-language sources (de))
[Applications of the p-adic Theory in Noncommutative Algebras]. Monatshefte für Mathematik (in German). 44: 203–224. Witt, Ernst (1935). "Riemann-Rochscher Satz und...
127 KB (14,714 words) - 12:12, 9 September 2024
(1910–1998) Shiing-Shen Chern (1911–2004) – differential geometry Ernst Witt (1911–1991) Rafael Artzy (1912–2006) Aleksandr Danilovich Aleksandrov (1912–1999)...
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the gauge group of the theory. Associated with any Lie group is the Lie algebra of group generators. For each group generator there necessarily arises...
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S2CID 119143902. Bhatt, Bhargav; Scholze, Peter (2017). "Projectivity of the Witt vector affine Grassmannian". Inventiones Mathematicae. 209 (2): 329–423....
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(Boolean algebra) Shannon's source coding theorem (information theory) Shell theorem (physics) Shirshov–Cohn theorem (Jordan algebras) Shirshov–Witt theorem...
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provided that dim(X)<p and X admits a smooth proper lift over the ring of Witt vectors W2(k) of length two (for example, for k=Fp, this ring would be Z/p2)...
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