Notes on Koszul duality (for quadratic algebras)
نویسنده
چکیده
3 Koszul duality 22 3.1 Quadratic algebras . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.2 Dual coalgebra and algebra . . . . . . . . . . . . . . . . . . . . . 23 3.3 Some more examples . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.3.1 The free algebra . . . . . . . . . . . . . . . . . . . . . . . 28 3.3.2 An example from Fröberg . . . . . . . . . . . . . . . . . . 28 3.3.3 The symmetric algebra . . . . . . . . . . . . . . . . . . . . 29 3.3.4 Quantum stuff . . . . . . . . . . . . . . . . . . . . . . . . 29 3.3.5 Limits of Gröbner basis . . . . . . . . . . . . . . . . . . . 30 3.3.6 The Sklyanin algebra . . . . . . . . . . . . . . . . . . . . . 30 3.3.7 No bounds for linear resolutions . . . . . . . . . . . . . . 30 3.4 Koszul at the bar . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.5 The Koszul resolution . . . . . . . . . . . . . . . . . . . . . . . . 32 3.6 Koszulity and rewriting . . . . . . . . . . . . . . . . . . . . . . . 33 3.7 Hilbert series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.8 Quadratic-linear algebras . . . . . . . . . . . . . . . . . . . . . . 36 3.9 Minimal models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3.10 A∞-algebras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
منابع مشابه
Koszul duality in deformation quantization and Tamarkin’s approach to Kontsevich formality
Let α be a quadratic Poisson bivector on a vector space V . Then one can also consider α as a quadratic Poisson bivector on the vector space V ∗[1]. Fixed a universal deformation quantization (prediction of some complex weights to all Kontsevich graphs [K97]), we have deformation quantization of the both algebras S(V ∗) and Λ(V ). These are graded quadratic algebras, and therefore Koszul algebr...
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تاریخ انتشار 2013