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Dualities on Generalized Koszul Algebras (Memoirs of the American Mathematical Society, No. 754) by Edward L. Green, Idun Reiten, Oyvind Solberg is a nonfiction available to read on EtoBox.

What is Dualities on Generalized Koszul Algebras (Memoirs of the American Mathematical Society, No. 754) about?

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

Who reads Dualities on Generalized Koszul Algebras (Memoirs of the American Mathematical Society, No. 754)?

Author

Edward L. Green, Idun Reiten, Oyvind Solberg

Publisher

American Mathematical Society

Published

2002

Language

EN

ISBN

9780821829349

Category

nonfiction

Subjects

Mathematics, Science, Stem