Regular modules over 2-dimensional quantum Beilinson algebras of Type \(S\)
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- 作者：Izuru Mori (1)
1. Department of Mathematics ; Graduate School of Science ; Shizuoka University ; Shizuoka ; 422-8529 ; Japan - 关键词：Regular modules ; Beilinson algebras ; AS ; regular algebras ; Representation infinite algebras ; Preprojective algebras ; 16G60 ; 16S38 ; 16S36 ; 16W50 ; 14A22
- 刊名：Mathematische Zeitschrift
- 出版年：2015
- 出版时间：April 2015
- 年：2015
- 卷：279
- 期：3-4
- 页码：1143-1174
- 全文大小：394 KB
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- 刊物主题：Mathematics
Mathematics - 出版者：Springer Berlin / Heidelberg
- ISSN：1432-1823
文摘
In the study of a finite dimensional hereditary algebra of infinite representation type, understanding regular modules is essential. Recently, Herschend, Iyama and Oppermann introduced the notions of \(d\) -representation infinite algebra and \(d\) -regular module, extending the above notions to finite dimensional algebras of global dimension \(d\ge 1\) . Since the Beilinson algebras of AS-regular algebras of dimension \(d+1\) are typical examples of \(d\) -representation infinite algebras, the purpose of this paper is to study the behavior of \(d\) -regular modules over such algebras. In particular, we will show that the isomorphism classes of simple 2-regular modules over a 2-representation tame quantum Beilinson algebra of Type \(S\) are parameterized by \({\mathbb {P}}^{2}\) .