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Notes on nonpure piecewise-Koszul algebras

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Abstract

Let A = ⊕i≥0 A i be a Noetherian standard graded algebra with finite global dimension, gr o(A) and \(\mathcal{N}\mathcal{P}\mathcal{K}(A)\) the categories of finitely 0-generated graded A-modules and nonpure piecewise-Koszul modules. It is proved that \(gr_0 (A) = \mathcal{N}\mathcal{P}\mathcal{K}(A)\), which implies that all the Noetherian standard graded Artin-Schlter regular algebras are nonpure piecewise-Koszul. Moreover, the H-Galois graded extension of nonpure piecewise-Koszul algebras is discussed, where H is a finite dimensional semisimple and cosemisimple Hopf algebra.

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang, 321004, P.R. China

    Jia-Feng Lü

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  1. Jia-Feng Lü
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Correspondence to Jia-Feng Lü.

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This work was supported by National Natural Science Foundation of China (11001245, 11271335 and 11101288).

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Lü, JF. Notes on nonpure piecewise-Koszul algebras. Indian J Pure Appl Math 46, 349–357 (2015). https://doi.org/10.1007/s13226-015-0114-y

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