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

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...

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

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

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

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

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...

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...

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...

(d. 2018) Bob Dawson, Australian rules footballer (d. 2023) Jean-Louis Koszul, French mathematician (d. 2018) John Russell, American actor (d. 1991) Cecil...

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...

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

connection on a smooth vector bundle E → X {\displaystyle E\to X} written as a Koszul connection on the C ∞ ( X ) {\displaystyle C^{\infty }(X)} -module of sections...

correspondence or BGG correspondence for short is the first example of the Koszul duality. Established by Joseph Bernstein, Israel Gelfand, and Sergei Gelfand...

suited for computations." The Čech complex can be defined as a colimit of Koszul complexes K ∙ ( f 1 , … , f m ) {\displaystyle K^{\bullet }(f_{1},\ldots...

{\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 ) ) −...

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...

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

version) was introduced by Ginzburg & Kapranov (1994) in their formulation of Koszul duality. Fix a base field k and let L i e ( x 1 , … , x n ) {\displaystyle...

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

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

{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...

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...

tensor algebra over the Hochschild homology of A. A Zinbiel algebra is the Koszul dual concept to a Leibniz algebra. It has as defining identity: ( a ∘ b...

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

but fattened. If r1, ..., rd is a regular sequence in a ring R, then the Koszul complex is an explicit free resolution of R/(r1, ..., rd) as an R-module...

Regular local ring Regular sequence Cohen–Macaulay ring Gorenstein ring Koszul complex Spectrum of a ring Zariski topology Kähler differential Generic...

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...