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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
mathematics, Drinfeld reciprocity, introduced by Drinfeld (1974), is a correspondence between eigenforms of the moduli space of Drinfeld modules and factors
Drinfeld_reciprocity
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
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
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
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
\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
Algebra with braided rigid category of representations
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
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
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
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
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)
American mathematician
Workplaces MIT Thesis The Mordell-Weil theorem, rigidity, and pairings for Drinfeld modules (1994) Doctoral advisor Kenneth Alan Ribet Doctoral students Kirsten
Bjorn_Poonen
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
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
Romanian-American mathematician
to Drinfeld modules and, more generally, to abelian t-motives. This formula generalizes and refines Lenny Taelman's class-number formula for Drinfeld modules
Cristian_Dumitru_Popescu
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
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
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
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
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
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
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
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
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
{\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
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
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
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)
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
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
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)
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
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
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
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
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
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
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
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
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)
theorem (algebraic topology) Leray's theorem (algebraic geometry) Manin–Drinfeld theorem (number theory) Max Noether's theorem (algebraic geometry) Mazur's
List_of_theorems
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
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
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)
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
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
Relate the direct image and the pull-back of sheaves
B'=B\otimes _{A}A'} . In this situation, given a B-module M, there is an isomorphism (of A'-modules): ( M ⊗ B B ′ ) A ′ ≅ ( M A ) ⊗ A A ′ . {\displaystyle
Base_change_theorems
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)
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 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 (in French)
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
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
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
travel, tourism, insurance
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