| Piecewise-Koszul algebras |
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| 引用本文： | Jia-feng L~1 Ji-wei HE~2 Di-ming LU~(1 ) ~1 Department of Mathematics,Zhejiang University,Hangzhou 310027,China,~2 Department of Mathematics,Shaoxing College of Arts and Sciences,Shaoxing 312000,China. Piecewise-Koszul algebras[J]. 中国科学A辑(英文版), 2007, 50(12): 1795-1804. DOI: 10.1007/s11425-007-0136-y |
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| 作者姓名： | Jia-feng L~1 Ji-wei HE~2 Di-ming LU~(1 ) ~1 Department of Mathematics Zhejiang University Hangzhou 310027 China ~2 Department of Mathematics Shaoxing College of Arts and Sciences Shaoxing 312000 China |
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| 摘 要： | 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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| 关 键 词： | A∞-algebras |
Piecewise-Koszul algebras |
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| Jia-feng Lü,Ji-wei He,Di-ming Lu. Piecewise-Koszul algebras[J]. Science in China(Mathematics), 2007, 50(12): 1795-1804. DOI: 10.1007/s11425-007-0136-y |
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| Authors: | Jia-feng Lü Ji-wei He Di-ming Lu |
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| Affiliation: | 1. Department of Mathematics, Zhejiang University, Hangzhou 310027, China
2. Department of Mathematics, Shaoxing College of Arts and Sciences, Shaoxing 312000, China |
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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. The work was supported by the National Natural Science Foundation of China (Grant No. 10571152) |
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| Keywords: | (d-)Koszul algebras Yoneda-Ext algebras |
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