Splitting algebras: Koszul, Cohen–Macaulay and numerically Koszul
نویسندگان
چکیده
منابع مشابه
Selfinjective Koszul Algebras
The study of Koszul algebras and their representations has accelerated significantly in the last few years. They have been used in Topology, Algebraic Geometry and Commutative Algebra and they are used more and more frequently in Representation Theory, see for instance [BGS],[GTM],[M],[MZ] and [R]. The aim of this paper is to present some of the results presented by the second author at the Lum...
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The algebras Qn describe the relationship between the roots and coefficients of a non-commutative polynomial. I.Gelfand, S.Gelfand, and V. Retakh have defined quotients of these algebras corresponding to graphs. In this work we find the Hilbert series of the class of algebras corresponding to the n-vertex path, Pn. We also show this algebra is Koszul. We do this by first looking at class of qua...
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Koszul algebras, introduced by Priddy in [P], are positively graded Kalgebras R whose residue field K has a linear free resolution as an R-module. Here linear means that the non-zero entries of the matrices describing the maps in the R-free resolution of K have degree 1. For example, the polynomial ring S = K[x1, . . . ,xn] over a field K (i.e the symmetric algebra SymK(V ) of a n-dimensional K...
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Quadratic algebras associated to graphs have been introduced by I. Gelfand, S. Gelfand, and Retakh in connection with decompositions of noncommutative polynomials. Here we show that, for each graph with rare triangular subgraphs, the corresponding quadratic algebra is a Koszul domain with global dimension equal to the number of vertices of the graph.
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We show that diagonal subalgebras and generalized Veronese subrings of a bigraded Koszul algebra are Koszul. We give upper bounds for the regularity of sidediagonal and relative Veronese modules and apply the results to symmetric algebras and Rees rings.
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2015
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2014.08.050