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《曹锡华代数论坛》系列报告

演讲人：浙江大学数学系、数学研究中心教授，浙江大学高等数学研究所副所长、新世纪优秀人才支持计划获得者李方教授
题目：Approach to artinian algebras via natural quivers and generalized modulations
地点：闵行数学楼102报告厅
时间：6月15日上午10：00---11：00
摘要： The method of quiver, e.g. Ext-quiver, is important for representations of an Artinian algebra. However, Ext-quiver is defined only over an algebraically closed field. This is the reason the so-called diagram, rather than valued quiver, of an artinian algebra was introduced by Dlab and Kirichenko. On the other hand, for the structure of an artinian algebra, the Ext-quiver is available only when this algebra is basic. In order to overcome this deficiency, we give the notion of natural quiver of an artinian algebra.
In this talk, we get the generalized Gabriel theorem for artinian algebras rather than basic algebras via generalized path algebras. And, the relation between natural quiver and Ext-quiver of an artinian algebra is characterized; also, the relation between natural quiver and diagram of an artinian algebra is discussed. Moreover, using of generalized modulations, we introduce the so-called natural valued quiver of an artinian algebra, which is just the valued Ext-quiver when the artinian algebra is basic.