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Piecewise-Koszul algebras

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Abstract

It is a small step toward the Koszul-type algebras. The piecewise-Koszul algebras are, in general, a new class of quadratic algebras but not the classical Koszul ones, simultaneously they agree with both the classical Koszul and higher Koszul algebras in special cases. We give a criteria theorem for a graded algebra A to be piecewise-Koszul in terms of its Yoneda-Ext algebra E(A), and show an A ∞-structure on E(A). Relations between Koszul algebras and piecewise-Koszul algebras are discussed. In particular, our results are related to the third question of Green-Marcos.

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang University, Hangzhou, 310027, China

    Jia-feng Lü & Di-ming Lu

  2. Department of Mathematics, Shaoxing College of Arts and Sciences, Shaoxing, 312000, China

    Ji-wei He

Authors
  1. Jia-feng Lü
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  2. Ji-wei He
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  3. Di-ming Lu
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Correspondence to Di-ming Lu.

Additional information

The work was supported by the National Natural Science Foundation of China (Grant No. 10571152)

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Lü, Jf., He, Jw. & Lu, Dm. Piecewise-Koszul algebras. Sci. China Ser. A-Math. 50, 1795–1804 (2007). https://doi.org/10.1007/s11425-007-0136-y

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  • DOI: https://doi.org/10.1007/s11425-007-0136-y

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