On a class of nontriangular representation-finite algebras forming an open Z-scheme

[摘要] The article is related with the question if representation-finite algebras form an open Z-scheme in the sense of Jensen and Lenzing (1989) [12, Chapter 12]. We define a class T MCL of algebras and we give the positive answer to the question restricted to that class. This is carried out by applying van den Dries' test. Let V be a valuation ring in an algebraically closed field K with the residue field R. Given a V-order 21, we denote by 24 the R-algebra obtained from U by reduction modulo the radical of V and U((K)) = U circle times(V) K. One of the main results asserts that if the R-algebra (U) over bar is representation-finite and belongs to the class T MCL then the K-algebra U((K)) is representation-finite and belongs to T MCL. It follows that the representation-finite algebras in T MCL form an open Z-scheme. (c) 2010 Elsevier B.V. All rights reserved.

[发布日期] 2010-12-01