Combinatorial classification of (± 1)-skew projective spaces

2021/07/27 by Akihiro Higashitani, Higashitani, Akihiro, Kenta Ueyama +1
Mathematics · #Finite Group Theory Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models

paper · pdf · doi:10.48550/arxiv.2107.12927

Abstract

The noncommutative projective scheme \operatorname\mathsfProj_nc S of a (± 1)-skew polynomial algebra S in n variables is considered to be a (± 1)-skew projective space of dimension n-1. In this paper, using combinatorial methods, we give a classification theorem for (± 1)-skew projective spaces. Specifically, among other equivalences, we prove that (± 1)-skew projective spaces \operatorname\mathsfProj_nc S and \operatorname\mathsfProj_nc S' are isomorphic if and only if certain graphs associated to S and S' are switching (or mutation) equivalent. We also discuss invariants of (± 1)-skew projective spaces from a combinatorial point of view.

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