2021/07/08 by Andrew K. Conner, Andrew Conner, Conner, Andrew +3
Mathematics · #16S37 (Primary) #16W50 (Secondary) #Advanced Topics in Algebra #Algebra over a field #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Algebraically closed field #Crystallography #FOS: Mathematics #Field (mathematics) #Geometry #Isomorphism (crystallography) #Mathematical analysis #Mathematics #Physics #Pure mathematics #Quadratic equation #Quantum #Quantum Algebra (math.QA) #Quantum mechanics #Rings and Algebras (math.RA) #Scheme (mathematics) #Subalgebra #Tensor (intrinsic definition) #Tensor product #Type (biology) #math.QA #math.RA #msc:16S37 #msc:16W50
paper · pdf · doi:10.48550/arxiv.2107.03612
published in arXiv (Cornell University) (Cornell University) · 40 pages, 3 tables, submitted
arxiv created 2021/07/08 · openalex publication_date 2021/07/08 · arxiv updated 2021/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let \mathbbk be an algebraically closed field. Building upon previous work, we classify, up to isomorphism of graded algebras, quadratic graded twisted tensor products of \mathbbk[x,y] and \mathbbk[z]. When such an algebra is Artin-Schelter regular, we identify its point scheme and type. We also describe which three-dimensional Sklyanin algebras contain a subalgebra isomorphic to a quantum ℙ1, and we show that every algebra in this family is a graded twisted tensor product of \mathbbk-1[x,y] and \mathbbk[z].