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Showing 1 to 6 of 6 for “"Koszul algebra"”.
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Graphs and Noncommutative Koszul Algebras
… between combinatorics and noncommutative algebra is established by relating a certain class of directed graphs to noncommutative Koszul algebras. The directed graphs in this class are called full graphs and are defined by a set of criteria on the edges. The structural properties of full …
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Generalized Koszul Properties of Commutative Local Rings
… local rings that generalize the notion of Koszul algebra. The properties are expressed in terms of the Ext algebra of the ring, or in terms of homological properties of powers of the maximal ideal of the ring. We analyze relationships between these properties and we identify large classes …
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Koszul Homology and Resolutions over Commutative Rings
<p>The Koszul homology algebra of a commutative local (or graded) ring R tends to reflect important information about the ring R and its properties. We examine Koszul homology and the relationship between Koszul homology and minimal free resolutions in various settings. We provide tools which allow …
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A Classification of some Quadratic Algebras
In this paper, for a select group of quadratic algebras, we investigate restrictions necessary on the generators of the ideal for the resulting algebra to be Koszul. Techniques include the use of Gröbner bases and development of Koszul resolutions. When the quadratic algebra is Koszul, we provide …
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Hochschild Cohomology Of Short Gorenstein Rings
… cohomology of the family of short Gorenstein k-algebras </p><p>sGor(N) =k[X_0,...,X_N](X_iX_j, X_i^2−X_j^2 | i,j= 0,...,N, i different from j), N≥2,</p><p>exhibits exponential growth. The proof uses Gröbner-Shirshov basis theory and along the way we describe an explicit monomial basis for the …
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Hochschild Cohomology of Short Gorenstein Rings
… cohomology of the family of short Gorenstein k-algebras </p><p>sGor(N) =k[X_0,...,X_N](X_iX_j, X_i^2−X_j^2 | i,j= 0,...,N, i different from j), N≥2,</p><p>exhibits exponential growth. The proof uses Gröbner-Shirshov basis theory and along the way we describe an explicit monomial basis for the …