Piecewise-Koszul algebras

Details Piecewise-Koszul algebras Piecewise-Koszul algebras

2011-09-17

arxiv.org/abs/1109.3761v1

Science in China, (2007)

Mathematics

Rings and Algebras

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Scientific paper

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 $A_{\infty}$-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' [6].

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