In mathematics, Koszul duality, named after the French mathematician Jean-Louis Koszul, is any of various kinds of dualities found in representation theory...

days after his 97th birthday. Koszul algebra Koszul complex Koszul duality Koszul cohomology Koszul connection Koszul–Tate resolution Lie algebra cohomology...

In mathematics, the Koszul complex was first introduced to define a cohomology theory for Lie algebras, by Jean-Louis Koszul (see Lie algebra cohomology)...

In mathematics, the Koszul cohomology groups K p , q ( X , L ) {\displaystyle K_{p,q}(X,L)} are groups associated to a projective variety X with a line...

In abstract algebra, a Koszul algebra R {\displaystyle R} is a graded k {\displaystyle k} -algebra over which the ground field k {\displaystyle k} has...

In mathematics, a Koszul–Tate resolution or Koszul–Tate complex of the quotient ring R/M is a projective resolution of it as an R-module which also has...

Julien Koszul (4 December 1844 – 15 January 1927) was a French composer and pipe organist from Alsace. Born in Morschwiller-le-Bas, Alsace, Koszul studied...

may be explicitly defined by either the second Christoffel identity or Koszul formula as obtained in the proofs below. This explicit definition expresses...

connections are also called Koszul connections after Jean-Louis Koszul, who gave an algebraic framework for describing them (Koszul 1950). This article defines...

nth syzygy module is free, but not the (n − 1)th one (for a proof, see § Koszul complex, below). The theorem is also true for modules that are not finitely...

Beilinson, Ginzburg, and Wolfgang Soergel introduced the concept of Koszul duality (cf. Koszul algebra) and the technique of "mixed categories" to representation...

Koszul (Koszul 1950) gave an algebraic framework for regarding a connection as a differential operator by means of the Koszul connection. The Koszul connection...

{\displaystyle 2g(\nabla _{X}Y,Z)-g([X,Y],Z)+g([X,Z],Y)+g([Y,Z],X)} . Thus, the Koszul formula g ( ∇ X Y , Z ) = 1 2 { X ( g ( Y , Z ) ) + Y ( g ( Z , X ) ) −...

in mathematics), Adrien Douady, Roger Godement, Max Karoubi, Jean-Louis Koszul, Jean-Pierre Serre and René Thom. Cartan's first research interests, until...

1950, Jean-Louis Koszul unified these new ideas of covariant differentiation in a vector bundle by means of what is known today as a Koszul connection or...

consequence of an explicit computation of a local cohomology by means of Koszul complexes (see below). ◻ {\displaystyle \square } Let R be a ring and x...

inspired by the Bourbaki seminars on mathematics. Henri Cartan, Les travaux de Koszul, I (Lie algebra cohomology) Claude Chabauty, Le théorème de Minkowski-Hlawka...

University of La Rioja. Cabezón obtained his PhD with the thesis "Combinatorial Koszul homology: computations and applications" for which he obtained the grade...

difficult theory both of formal and of analytical structure. This is a kind of Koszul complex theory, taken up by numerous mathematicians during the 1960s. In...

quantum groups. The most important class of graded quadratic algebras is Koszul algebras. A graded quadratic algebra A is determined by a vector space of...

{g}}\to C^{\infty }(M)} of the Hamiltonian action. The resulting Koszul complex is the Koszul complex of the S ( g ) {\displaystyle S({\mathfrak {g}})} -module...

is the quotient of a commutative ring by any regular sequence, using the Koszul complex. For example, if R is the polynomial ring k[x1,...,xn] over a field...

differential geometry Magnus Wenninger (1919–2017) – polyhedron models Jean-Louis Koszul (1921–2018) Isaak Yaglom (1921–1988) Eugenio Calabi (1923–2023) Benoit Mandelbrot...

Barsotti–Tate group Birch–Tate conjecture Hodge-Tate module Honda–Tate theorem Koszul–Tate resolution Lubin–Tate formal group law Néron–Tate height Sato-Tate...

Calyampudi Radhakrishna Rao Harold Jeffreys Solomon Kullback Jean-Louis Koszul Richard Leibler Claude Shannon Imre Csiszár Nikolai Chentsov (also written...

; Knapen, M.; Hanot-Mambres, D.; Heuskin, A.-C.; Pineux, F.; Lucas, S.; Koszul, R.; van Doninck, K. (July 2014). "Gateway to genetic exchange? DNA double-strand...

generalized to higher order syzygy modules, and this leads to the concept of the Koszul complex of an ideal, which provides information on the non-trivial relations...

with their own parallel transportation systems as well. For instance, a Koszul connection in a vector bundle also allows for the parallel transport of...

Hespeels B, Knapen M, Hanot-Mambres D, Heuskin AC, Pineux F, LUCAS S, Koszul R, Van Doninck K (July 2014). "Gateway to genetic exchange? DNA double-strand...

Poczobut w drużynie Czarnych Koszul - Oficjalna strona Polonii Warszawa". Bartłomiej Poczobut w drużynie Czarnych Koszul - Oficjalna strona Polonii Warszawa...