Dualities on Generalized Koszul Algebras
Seiten
2002
American Mathematical Society (Verlag)
9780821829349 (ISBN)
American Mathematical Society (Verlag)
9780821829349 (ISBN)
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Koszul rings are graded rings which have played an important role in algebraic topology, noncommutative algebraic geometry and in the theory of quantum groups. One aspect of the theory is to compare the module theory for a Koszul ring and its Koszul dual. There are dualities between subcategories of graded modules; the Koszul modules.
Koszul rings are graded rings which have played an important role in algebraic topology, algebraic geometry, noncommutative algebraic geometry, and in the theory of quantum groups. One aspect of the theory is to compare the module theory for a Koszul ring and its Koszul dual. There are dualities between subcategories of graded modules; the Koszul modules. When $/Lambda$ is an artin algebra and $T$ is a cotilting $/Lambda$-module, the functor $/mathrm{Hom}_/Lambda(/,T)$ induces a duality between certain subcategories of the finitely generated modules over $/Lambda$ and $/mathrm{End}_/Lambda(T)$. The purpose of this paper is to develop a unified approach to both the Koszul duality and the duality for cotilting modules.This theory specializes to these two cases and also contains interesting new examples. The starting point for the theory is a positively $/mathbb{Z}$-graded ring $/Lambda=/Lambda_0+/Lambda_1+/Lambda_2+/cdots$ and a (Wakamatsu) cotilting $/Lambda_0$-module $T$, satisfying additional assumptions. The theory gives a duality between certain subcategories of the finitely generated graded modules generated in degree zero over $/Lambda$ on one hand and over the Yoneda algebra $/oplus_{i/geq 0} /mathrm{Ext}^i_/Lambda(T,T)$ on the other hand.
Koszul rings are graded rings which have played an important role in algebraic topology, algebraic geometry, noncommutative algebraic geometry, and in the theory of quantum groups. One aspect of the theory is to compare the module theory for a Koszul ring and its Koszul dual. There are dualities between subcategories of graded modules; the Koszul modules. When $/Lambda$ is an artin algebra and $T$ is a cotilting $/Lambda$-module, the functor $/mathrm{Hom}_/Lambda(/,T)$ induces a duality between certain subcategories of the finitely generated modules over $/Lambda$ and $/mathrm{End}_/Lambda(T)$. The purpose of this paper is to develop a unified approach to both the Koszul duality and the duality for cotilting modules.This theory specializes to these two cases and also contains interesting new examples. The starting point for the theory is a positively $/mathbb{Z}$-graded ring $/Lambda=/Lambda_0+/Lambda_1+/Lambda_2+/cdots$ and a (Wakamatsu) cotilting $/Lambda_0$-module $T$, satisfying additional assumptions. The theory gives a duality between certain subcategories of the finitely generated graded modules generated in degree zero over $/Lambda$ on one hand and over the Yoneda algebra $/oplus_{i/geq 0} /mathrm{Ext}^i_/Lambda(T,T)$ on the other hand.
Main results and examples Proofs of main results Generalized $T$-Koszul algebras Further results and questions Bibliography.
| Erscheint lt. Verlag | 1.9.2002 |
|---|---|
| Reihe/Serie | Memoirs of the American Mathematical Society |
| Verlagsort | Providence |
| Sprache | englisch |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-13 | 9780821829349 / 9780821829349 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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