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The representation theory of Dynkin quivers and the Freudenthal-Tits magic square

Claus Michael Ringel 教授(德国比勒费尔德大学)
2016-11-30(周三)15:00-16:00  闵行校区数学楼401报告厅
 
报告人简介:

国际代数表示论权威专家、德国比勒费尔德大学教授、上海交大访问讲座教授。

报告内容简介:

Let Q be a Dynkin quiver of type E with exceptional vertex y and Q' the quiver obtained from Q by deleting y. Let M be the maximal indecomposable representation of Q. The restriction of M to Q' turns out to be the direct sum of three pairwise orthogonal indecomposable representations A(1), A(2), A(3). These representations seem to play a decisive role in the representation theory of the Dynkin quiver Q and of the corresponding Euclidean quiver. The lecture will provide a characterization of this antichain triple. Note that the reduction scheme follows the rules of the magic Freudenthal-Tits square-thus it relates the exceptional Dynkin quivers to the Euclidean Hurwitz algebras (the complex numbers, the quaternions and the octonions). We will discuss in which way the octonions may be reconstructed using the representation theory of E_6.


主持人:胡乃红 教授
   
 
 
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