We study the syzygies of Koszul algebras. The main result asserts that a Koszul algebra has syzygies whose degrees growth as the degrees of the syzygies of a complete intersection of quadrics. More precisely, if R is a Koszul algebra and t_i is the largest degree of a i-th syzygy of R, we show that t_i is at most 2i.
Free resolutions over commutative Koszul algebras
CONCA, ALDO;
2010-01-01
Abstract
We study the syzygies of Koszul algebras. The main result asserts that a Koszul algebra has syzygies whose degrees growth as the degrees of the syzygies of a complete intersection of quadrics. More precisely, if R is a Koszul algebra and t_i is the largest degree of a i-th syzygy of R, we show that t_i is at most 2i.
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