Abstract
We use a representation of a graded twisted tensor product of K[x] with K[y] in \(L(K^{\mathbb {N}_{0}})\) 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.
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We thank the anonymous referee for the thorough revision and numerous helpful suggestions.
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Presented by: Vyjayanthi Chari
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Christian Valqui was supported by PUCP-DGI-2019-1-0015.
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Bances, R., Valqui, C. On the Classification of Graded Twisted Planes. Algebr Represent Theor 26, 1231–1270 (2023). https://doi.org/10.1007/s10468-022-10131-8
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DOI: https://doi.org/10.1007/s10468-022-10131-8