TY - JOUR
T1 - On the Classification of Graded Twisted Planes
AU - Bances, Ricardo
AU - Valqui, Christian
N1 - Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Nature B.V.
PY - 2023/8
Y1 - 2023/8
N2 - We use a representation of a graded twisted tensor product of K[x] with K[y] in L(Kℕ0) in order to obtain a nearly complete classification of these graded twisted tensor products via infinite matrices. There is one particular example and three main cases: quadratic algebras classified in Conner and Goetz (J. Noncommut. Geom. 15(1), 41–78, 2021), a family called A(n, d, a) with the n + 1-extension property for n ≥ 2, and a third case, not fully classified, which contains a family B(a, L) parameterized by quasi-balanced sequences.
AB - We use a representation of a graded twisted tensor product of K[x] with K[y] in L(Kℕ0) in order to obtain a nearly complete classification of these graded twisted tensor products via infinite matrices. There is one particular example and three main cases: quadratic algebras classified in Conner and Goetz (J. Noncommut. Geom. 15(1), 41–78, 2021), a family called A(n, d, a) with the n + 1-extension property for n ≥ 2, and a third case, not fully classified, which contains a family B(a, L) parameterized by quasi-balanced sequences.
KW - Quadratic algebras
KW - Twisted tensor products
UR - http://www.scopus.com/inward/record.url?scp=85129291554&partnerID=8YFLogxK
U2 - 10.1007/s10468-022-10131-8
DO - 10.1007/s10468-022-10131-8
M3 - Article
AN - SCOPUS:85129291554
SN - 1386-923X
VL - 26
SP - 1231
EP - 1270
JO - Algebras and Representation Theory
JF - Algebras and Representation Theory
IS - 4
ER -