Quantum projective planes as certain graded twisted tensor products.

Let K be an algebraically closed field. Building upon previous work, we classify, up to isomorphism of algebras, quadratic graded twisted tensor products of K [ x , y ] and K [ z ]. When such an algebra is Artin-Schelter regular, we identify its point scheme and type, in the sense of [6]. We also describe which three-dimensional Sklyanin algebras contain a subalgebra isomorphic to a quantum P 1 , and we show that every algebra in this family is a graded twisted tensor product of K − 1 [ x , y ] and K [ z ]. [ABSTRACT FROM AUTHOR]