(p, λ)-Koszul algebras and modules

Jia-Feng Lü () and Zhi-Bing Zhao ()
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Jia-Feng Lü: Zhejiang Normal University
Zhi-Bing Zhao: Anhui University

Indian Journal of Pure and Applied Mathematics, 2010, vol. 41, issue 3, 443-473

Abstract: Abstract In this paper, the notions of (p, λ)-Koszul algebra and (p, λ)-Koszul module are introduced. Some criteria theorems for a positively graded algebra A to be (p, λ)-Koszul are given. The notion of weakly (p, λ)-Koszul module is defined as well and let WK λ p (A) denote the category of weakly (p, λ)-Koszul modules. We show that M ∈ WK λ p (A) if and only if it can be approximated by (p, λ)-Koszul submodules, which is equivalent to that G(M) is a (p, λ)-Koszul module, where G(M) denotes the associated graded module of M. As applications, the relationships of the minimal graded projective resolutions of M, G(M) and (p, λ)-Koszul submodules are established. In particular, for a module M ∈ WK λ p (A) we prove that ⊕i≥0 Ext A i (M,A 0) ∈ gr 0(E(A)), we also get as a consequence that the finitistic dimension conjecture is valid in WK λ p (A) under certain conditions.

Keywords: (p; λ)-Koszul algebras; Yoneda-Ext algebras; weakly (p; λ)-Koszul modules (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/s13226-010-0027-8

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