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- W2242335237 abstract "Let K be a field and let R4 5 i N Ri be a homogeneous K-algebra, that is, an algebra of the form K[x1 , R , xn ] /I where I is a homogeneous ideal. The minimal R-free resolution of a graded R-module M is said to be linear if the matrices that represent the maps of the resolution have entries of degree 1 . Recall that R is said to be Koszul if K has a linear R-free resolution. More generally, one says that R is universally Koszul (uk for short) if all the ideals of R generated by elements of degree 1 have a linear R-free resolution. For an updated survey on Koszul algebras we refer the reader to the recent paper of Froberg [F]. For generalities on uk algebras we refer the reader to [C]. Our goal is to classify the uk algebras defined by monomials. We recall first a few facts. Given two homogeneous K-algebras R4K[x1 , R , xn ] /I and S4K[y1 , R , ym ] /J the fiber product RiS of R and S is K[x1 , R , xn , y1 , R , ym ] /H where H4I1J1 (xi yj : i41, R , n and j41, R , m). One has [Lemma 1.6, C]:" @default.
- W2242335237 created "2016-06-24" @default.
- W2242335237 creator A5064915075 @default.
- W2242335237 date "2002-01-01" @default.
- W2242335237 modified "2023-09-26" @default.
- W2242335237 title "Universally Koszul algebras defined by monomials" @default.
- W2242335237 hasPublicationYear "2002" @default.
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