Regular modules over 2-dimensional quantum Beilinson algebras of Type $$S$$ S

Abstract

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 \({\mathbb {P}}^{2}\).