On Koszul Algebras and a New Construction of Artin–Schelter Regular Algebras

By B. Shelton, Craig T Tingey. 2001

64 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/6572aab4e46631dc138f48d3f8878e15273da42d

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In Algebra and Number Theory

1. Thomas Cassidy
2. Michaela Vancliff
3. B. Shelton

In Geometry and Topology

1. Thomas Cassidy
2. Michaela Vancliff
3. B. Shelton

In Statistical and Nonlinear Physics

1. Thomas Cassidy
2. Michaela Vancliff
3. B. Shelton

Citations in the corpus

• Generalizing the notion of Koszul algebra (2007, background): “If A has four generators then it is Koszul (see also [ 19 ]) and hence K2. If the algebra has two generatorsthenithastworelations,oneofdegree3andoneofdegree4and A K hasaminimal projective resolution of the form: 0 → A(−7) → A(−6) 2 → A(−3, −4) → A(−1) 2 → A → K → 0”
• Generalizations of graded Clifford algebras and of complete intersections (2010, methodology): “In particular, the solution −1 = μ13 = μ24, μ14 = μ23 = i, where i(2) = −1, together with q3 = z(2) 1 + z 2 3 + z2z4 and q4 = z 2 2 + z 2 4 + z1z3, yields a regular graded skew Clifford algebra that is an algebra presented in [9] and which has exactly twenty nonisomorphic point modules”