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Concept in mathematics
In mathematics, a Drinfeld module (or elliptic module) is roughly a special kind of module over a ring of functions on a curve over a finite field, generalizing
Drinfeld_module
Mathematician
forms, through the notions of elliptic module and the theory of the geometric Langlands correspondence. Drinfeld introduced the notion of a quantum group
Vladimir_Drinfeld
In mathematics a Yetter–Drinfeld category is a special type of braided monoidal category. It consists of modules over a Hopf algebra which satisfy some
Yetter–Drinfeld_category
analysis. It is used in the definition of the Carlitz module – an example of a Drinfeld module. We work over the polynomial ring Fq[T] of one variable
Carlitz_exponential
mathematics, Drinfeld reciprocity, introduced by Drinfeld (1974), is a correspondence between eigenforms of the moduli space of Drinfeld modules and factors
Drinfeld_reciprocity
Direct summand of a free module (mathematics)
free modules. In general, the precise relation between flatness and projectivity was established by Raynaud & Gruson (1971) (see also Drinfeld (2006)
Projective_module
\operatorname {Hom} _{R}(M,R)} . dualizing dualizing module Drinfeld A Drinfeld module is a module over a ring of functions on algebraic curve with coefficients
Glossary_of_module_theory
American mathematician
Institutions MIT Thesis The Mordell-Weil theorem, rigidity, and pairings for Drinfeld modules (1994) Doctoral advisor Kenneth Alan Ribet Doctoral students Kirsten
Bjorn_Poonen
Concept in Hopf algebra
discussed by M. Takeuchi in 1981, and now a general tool for construction of Drinfeld quantum double. Consider two bialgebras A {\displaystyle A} and X {\displaystyle
Bicrossed product of Hopf algebra
Bicrossed_product_of_Hopf_algebra
antipode of H is bijective. A Yetter–Drinfeld module R over H is called a braided bialgebra in the Yetter–Drinfeld category H H Y D {\displaystyle {}_{H}^{H}{\mathcal
Braided_Hopf_algebra
Finitely generated extension field of positive transcendence degree
algebraic variety function field (scheme theory) algebraic function Drinfeld module Gabriel Daniel & Villa Salvador (2007). Topics in the Theory of Algebraic
Algebraic_function_field
its dual, using the Drinfeld quantum double construction. If the Hopf algebra H is quasitriangular, then the category of modules over H is braided with
Quasitriangular_Hopf_algebra
French Canadian mathematician
random matrix theory, and she has shown interest in elliptic curves and Drinfeld modules. She is the 2013 winner of the Krieger–Nelson Prize, given annually
Chantal_David
Algebraic construct of interest in theoretical physics
kinds of noncommutative algebras with additional structure. These include Drinfeld–Jimbo type quantum groups (which are quasitriangular Hopf algebras), compact
Quantum_group
mathematics, a Lie-* algebra is a D-module with a Lie* bracket. They were introduced by Alexander Beilinson and Vladimir Drinfeld, and are similar to the conformal
Lie-*_algebra
quasi-isomorphic to a bounded complex of finite projective A-modules. A perfect module is a module that is perfect when it is viewed as a complex concentrated
Perfect_complex
Variant of the notion of the center of a monoid, group, or ring to a category
a branch of mathematics, the center (or Drinfeld center, after Soviet-American mathematician Vladimir Drinfeld) is a variant of the notion of the center
Center_(category_theory)
Series of mathematics textbooks
Stochastic Processes, Jean-François Le Gall (2022, ISBN 978-3-031-14205-5) Drinfeld Modules, Mihran Papikian (2023, ISBN 978-3-031-19706-2) Random Walks on Infinite
Graduate_Texts_in_Mathematics
Associative algebra generalizing the Virasoro algebra
an algebra that is obtained from g {\displaystyle {\mathfrak {g}}} by Drinfeld-Sokolov reduction. For any integer N ≥ 2 {\displaystyle N\geq 2} , the
W-algebra
Mathematics award
Archived from the original (PDF) on 6 October 2014. "Vladimir Gershonovich Drinfeld". Encyclopædia Britannica. 19 August 2009. Archived from the original on
Fields_Medal
Field of mathematics
equidistribution and invariant measures, especially on p-adic spaces. dynamics on Drinfeld modules. number-theoretic iteration problems that are not described by rational
Arithmetic_dynamics
{\displaystyle \tau _{V,W}} , most importantly the modules over quasitriangular Hopf algebras and Yetter–Drinfeld modules over finite groups (such as Z 2 {\displaystyle
Braided_vector_space
German-American mathematician and murder victim
Nichols Zoeller theorem for Hopf algebras in the category of Yetter Drinfeld modules", Communications in Algebra, 29 (6): 2481–2487, doi:10.1081/AGB-100002402
Bettina_Richmond
and Drinfeld (2004) as a rigorous version of the rather vague concept of a chiral algebra in physics. In Chiral Algebras, Beilinson and Drinfeld introduced
Chiral_algebra
American mathematician
with Dragoș Ghioca: Algebraic equations on the adèlic closure of a Drinfeld module. In: Israel J. Math., vol. 194, 2013, pp. 461–483. ArXiv Counting special
Thomas_W._Scanlon
Topic in algebraic number theory
{\displaystyle \{w_{1},\dots ,w_{m}\}} forms a group with the field addition. Drinfeld module Additive map Goss, David (1996), Basic Structures of Function Field
Additive_polynomial
Algebra used in 2D conformal field theories and string theory
Huang, Kriz, and others, D-module-theoretic objects called chiral algebras introduced by Alexander Beilinson and Vladimir Drinfeld and factorization algebras
Vertex_operator_algebra
found in the lecture of Heckenberger. Consider a Yetter–Drinfeld module V in the Yetter–Drinfeld category H H Y D {\displaystyle {}_{H}^{H}{\mathcal {YD}}}
Nichols_algebra
Topics referred to by the same term
"Walking Stuka" Shtuka, a sort of generalization of the mathematical Drinfeld module This disambiguation page lists articles associated with the title Stuka
Stuka_(disambiguation)
American mathematician
"Explicit Class Field Theory in Function Fields: Gross-Stark Units and Drinfeld Modules." She was then awarded a Churchill Scholarship to study for a year
Alison_Miller
American mathematician
1999 September 17 Died in Pittsburgh, PA The Carlitz module is generalized by the Drinfeld module An identity regarding Bernoulli numbers Carlitz wrote
Leonard_Carlitz
polynomial ring — this can be applied especially in the theory of Drinfeld modules. Let k {\displaystyle k} be a field of characteristic p {\displaystyle
Twisted_polynomial_ring
Russian-American mathematician
affine Kac–Moody algebras (these are also known as Wakimoto modules), defined the quantum Drinfeld-Sokolov reduction, and described the center of the universal
Edward_Frenkel
1985, Introduction Deligne, P.; Husemöller, D. (1987). "Survey of Drinfeld's modules" (PDF). Contemp. Math. 67 (1): 25–91. doi:10.1090/conm/067/902591
Level structure (algebraic geometry)
Level_structure_(algebraic_geometry)
spaces. Tate modules were introduced by Drinfeld (2006) to serve as a notion of infinite-dimensional vector bundles. For any ring R, Drinfeld defined elementary
Tate_vector_space
class#Complex projective space.) For this notion, see § 1 of A. Beilinson and V. Drinfeld, Quantization of Hitchin’s integrable system and Hecke eigensheaves [1]
Cotangent_sheaf
Hans-Jürgen (December 2010). "The Nichols algebra of a semisimple Yetter–Drinfeld module". American Journal of Mathematics. 132 (6): 1493–1547. arXiv:0803.2430
List of finite-dimensional Nichols algebras
List_of_finite-dimensional_Nichols_algebras
Russian-American mathematician
conjectures. From the early 1990s onwards, Beilinson worked with Vladimir Drinfeld to rebuild the theory of vertex algebras. After some informal circulation
Alexander_Beilinson
Quantum consistency equation
elliptic algebras respectively. Set-theoretic solutions were studied by Drinfeld. In this case, there is an R {\displaystyle R} -matrix invariant basis
Yang–Baxter_equation
Generalization of bialgebra
bialgebras: they were first defined by the Ukrainian mathematician Vladimir Drinfeld in 1990. A quasi-bialgebra differs from a bialgebra by having coassociativity
Quasi-bialgebra
Algebraic structure
Guide to Quantum Groups. Cambridge University Press. ISBN 0-521-55884-0. Drinfeld, Vladimir (1989). "Quasi-Hopf algebras". Leningrad Math J. 1: 1419–1457
Ribbon_Hopf_algebra
French mathematician
Vincent Lafforgue: L’isomorphisme entres les tours de Lubin-Tate et de Drinfeld, Birkhäuser, Progress in Mathematics, vol. 262, 2008 Filtration de monodromie
Laurent_Fargues
Mathematical concept
David; Francis, John; Nadler, David (2010), "Integral transforms and Drinfeld centers in derived algebraic geometry", Journal of the American Mathematical
Compact_object_(mathematics)
Mathematical structure
Heegner points on the classical modular curve X0(N) as well as on the Drinfeld modular curve XDrin 0(I). These buildings with complex multiplication are
Building_(mathematics)
Theory of a class of elliptic curves
point Hilbert's twelfth problem Lubin–Tate formal group, local fields Drinfeld shtuka, global function field case Wiles's proof of Fermat's Last Theorem
Complex_multiplication
Isomorphism of commutative rings constructed in the theory of Lie algebras
W-algebra constructed associated to the Langlands dual Lie algebra by Drinfeld–Sokolov reduction: Z ( g ^ ) ≅ W ( L g ) . {\displaystyle {\mathfrak {Z}}({\hat
Harish-Chandra_isomorphism
theorem (algebraic topology) Leray's theorem (algebraic geometry) Manin–Drinfeld theorem (number theory) Max Noether's theorem (algebraic geometry) Mazur's
List_of_theorems
S2CID 13514070. Lafforgue, Laurent (1998). "Chtoucas de Drinfeld et applications" [Drinfelʹd shtukas and applications]. Documenta Mathematica (in French)
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
British-Lebanese mathematician (1929–2019)
Bielawski (Berry–Robbins problem), Howard Donnelly (L-functions), Vladimir G. Drinfeld (instantons), Johan L. Dupont (singularities of vector fields), Lars Gårding
Michael_Atiyah
Czech mathematician
Prest, Mike; Trlifaj, Jan (2012), "Model category structures arising from Drinfeld vector bundles" (PDF), Advances in Mathematics, 231 (3–4): 1417–1438, doi:10
Jan_Trlifaj
Relate the direct image and the pull-back of sheaves
David; Francis, John; Nadler, David (2010), "Integral transforms and Drinfeld centers in derived algebraic geometry", J. Amer. Math. Soc., 23 (4): 909–966
Base_change_theorems
History of maths
Year Contributors Event 1890 David Hilbert Resolution of modules and free resolution of modules. 1890 David Hilbert Hilbert's syzygy theorem is a prototype
Timeline of category theory and related mathematics
Timeline_of_category_theory_and_related_mathematics
Two-dimensional conformal field theory
{\displaystyle SL_{2}(\mathbb {R} )} Wess–Zumino–Witten model by a quantum Drinfeld–Sokolov reduction. Moreover, correlation functions of the H 3 + {\displaystyle
Liouville_field_theory
French mathematician (born 1962)
Wiesława Nizioł). Cohomologie p {\displaystyle p} -adique de la tour de Drinfeld, le cas de la dimension 1, Journal of the AMS 33 (2020), 311–362 (with
Pierre_Colmez
Mathematical conjectures in class field theory
ISBN 978-0-691-03256-6, MR 1204652 Carayol, Henri (1992), "Variétés de Drinfeld compactes, d'après Laumon, Rapoport et Stuhler", Astérisque, 206: 369–409
Local_Langlands_conjectures
Mathematics course at the Collège de France
compacts et systèmes hamiltoniens 1995–1996 Laurent Lafforgue Chtoucas de Drinfeld et conjecture de Ramanujan-Petersson 1996–1997 Christophe Breuil Cohomologie
Peccot_Lectures
City in Ukraine
economist Andrey Denisov (born 1952) – Russian diplomat in China Vladimir Drinfeld (born 1954) – mathematician, awarded Fields Medal in 1990 Isaak Dunayevsky
Kharkiv
Pictorial representation of symmetry
1971, § 7 Algebraic geometry and number theory: in honor of Vladimir Drinfeld's 50th Birthday, edited by Victor Ginzburg, p. 47, section 3.6: Cluster
Dynkin_diagram
Mathematical set with some added structure
space Chu space Closure space Conformal space Complex analytic space Drinfeld's symmetric space Eilenberg–Mac Lane space Euclidean space Fiber space Finsler
Space_(mathematics)
DRINFELD MODULE
DRINFELD MODULE
Surname or Lastname
English
English : habitational name from any of numerous minor places named Greenfield, from Old English grēne ‘green’ + feld ‘pasture’, ‘open country’ (see Field).English : variant of Granville.English translation of German and Ashkenazic Jewish Grünfeld (see Grunfeld).
Surname or Lastname
English
English : topographic name from Middle English infeld ‘land near the homestead or village’, or a habitational name from any of various minor places named with this term, for example In Field in Humberside or Infield House in Lancashire.
DRINFELD MODULE
DRINFELD MODULE
Boy/Male
Gaelic Teutonic
From the north.
Boy/Male
Gaelic
Male
French
French and Galician-Portuguese form of Latin Alexandrus, ALEXANDRE means "defender of mankind."
Girl/Female
Hindu, Indian, Tamil
The World; The Other Name of Earth
Girl/Female
Hindu, Indian, Marathi, Sanskrit
Good Looking
Girl/Female
Arabic, Muslim
Guardian; Protector; Feminine of Hafeez
Girl/Female
Hindu
Boy/Male
Hindu
Boy/Male
Tamil
Lord of all virtues, Lord Ganesh
Girl/Female
Tamil
Without the limitations of form, Divine
DRINFELD MODULE
DRINFELD MODULE
DRINFELD MODULE
DRINFELD MODULE
DRINFELD MODULE
n.
The distance through the lower part of the shaft of a column, used as a standard measure for all parts of the order. See Module.
n.
To model; also, to modulate.
n.
A fixed part of a module. See Module.
a.
Having a space equal to two diameters or four modules between two columns; -- said of a portico or building. See Intercolumniation.
a.
Of or pertaining to mode, modulation, module, or modius; as, modular arrangement; modular accent; modular measure.
n.
A model or measure.
n.
The size of some one part, as the diameter of semi-diameter of the base of a shaft, taken as a unit of measure by which the proportions of the other parts of the composition are regulated. Generally, for columns, the semi-diameter is taken, and divided into a certain number of parts, called minutes (see Minute), though often the diameter is taken, and any dimension is said to be so many modules and minutes in height, breadth, or projection.