In mathematics, Koszul duality, named after the French mathematician Jean-Louis Koszul, is any of various kinds of dualities found in representation theory of Lie algebras, abstract algebras (semisimple algebra)[1] and topology (e.g., equivariant cohomology[2]). The prototype example is the BGG correspondence, due to Joseph Bernstein, Israel Gelfand, and Sergei Gelfand,.[3] It is a duality between the derived category of a symmetric algebra and that of an exterior algebra. The importance of the notion rests on the suspicion that Koszul duality seems quite ubiquitous in nature.[citation needed]
^Ben Webster, Koszul algebras and Koszul duality. November 1, 2007
^Mark Goresky, Robert Kottwitz, and Robert MacPherson. Equivariant cohomology, Koszul duality, and the localization theorem. Inventiones Mathematicae 131 (1998).
^Joseph Bernstein, Israel Gelfand, and Sergei Gelfand. Algebraic bundles over and problems of linear algebra. Funkts. Anal. Prilozh. 12 (1978); English translation in Functional Analysis and its Applications 12 (1978), 212-214
In mathematics, Koszulduality, named after the French mathematician Jean-Louis Koszul, is any of various kinds of dualities found in representation theory...
was introduced by Ginzburg & Kapranov (1994) in their formulation of Koszulduality. Fix a base field k and let L i e ( x 1 , … , x n ) {\displaystyle {\mathcal...
the French mathematician Jean-Louis Koszul. Koszulduality Complete intersection ring Fröberg, R. (1999), "Koszul algebras", Advances in commutative ring...
Beilinson, Ginzburg, and Wolfgang Soergel introduced the concept of Koszulduality (cf. Koszul algebra) and the technique of "mixed categories" to representation...
In mathematics, the Koszul complex was first introduced to define a cohomology theory for Lie algebras, by Jean-Louis Koszul (see Lie algebra cohomology)...
representation theory has important applications to Kazhdan-Lusztig theory and Koszulduality. The category of Soergel bimodules is named in his honor. His doctoral...
Moreover, Ext* S(k,k) is the polynomial ring R; this is an example of Koszulduality. By the general properties of derived functors, there are two basic...
cohomology of invariant differential forms does not yield new information. Koszulduality is known to hold between equivariant cohomology and ordinary cohomology...
ISBN 978-0-8218-3528-9. Beilinson, A. A.; Ginzburg, V.; Soergel, W. (1996). "Koszulduality patterns in representation theory". Journal of the American Mathematical...
Mikhail Kapranov discovered that some duality phenomena in rational homotopy theory could be explained using Koszulduality of operads. Operads have since found...
category of modules over DG-algebras. Keller also gives applications to Koszulduality, Lie algebra cohomology, and Hochschild homology. More generally, carefully...
1007/s10883-005-4170-1. S2CID 121944962. Ginzburg, V.; Kapranov, M. (1994). "Koszulduality for operads". Duke Math. J. 76: 203–273. arXiv:0709.1228. doi:10...
differential graded algebras. This duality between commutative algebras and Lie algebras is a version of Koszulduality. For spaces whose rational homology...
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...
The exterior algebra is the main ingredient in the construction of the Koszul complex, a fundamental object in homological algebra. The exterior algebra...
algebra as row-vectors, the same can be generalized to arbitrary pair of Koszuldual algebras and associated general Manin matrices. Observation 3. Cramer's...
_{R}} is a dualizing module for R {\displaystyle R} . In terms of the Matlis duality functor D ( − ) {\displaystyle D(-)} , the local duality theorem may...
André Weil, is a differential graded algebra given by the Koszul algebra Λ(g*)⊗S(g*) of its dual g*. Cartan, Henri (1951), "Notions d'algèbre différentielle;...
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