Classification of generalized \(A\)-graded algebras with 3 generators
type: Item
instance of: scholarly article
title: Classification of generalized \(A\)-graded algebras with 3 generators
zbMATH Open document ID: 0836.13002
author: Yanyan Li
published in: Bulletin des Sciences Mathématiques
publication date: 1995-10-04T00:00:00Z
review text: Let \(B\) be an \(N\)-graded algebra over the field \(\mathbb{C}\) of complex numbers generated by finitely many homogeneous elements \(x_1, \dots, x_n\) of degrees \(p_1, \dots, p_n\), respectively. \(B\) is called an \(A\)-graded algebra if all the nontrivial homogeneous subspaces of \(B\) have the dimension 1. For any linear function \(\varphi : R^n \to R\) and degrees \(p_1, \dots, p_n\) the authors construct an \(A\)-graded algebra \(B\) generated by \(n\) homogeneous elements of degrees \(p_1, \dots, p_n\). Extending results of V. I. Arnold the authors characterize all \(A\)-graded algebras generated by three elements in terms of linear functions. They show also that for every triple \((p_1, p_2, p_3)\) there are only finitely many \(A\)-graded algebras generated by three homogeneous elements of degrees \(p_1, p_2, p_3\), respectively.
Mathematics Subject Classification ID: 13A02
Mathematics Subject Classification ID: 13C15
zbMATH DE Number: 792812
zbMATH Keywords: graded algebras generated by three elements
reviewed by: Ánh Pham Ngoc
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 792812