Indecomposable Representations of Graphs and Algebras is popular PDF and ePub book, written by Vlastimil Dlab in 1976, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Indecomposable Representations of Graphs and Algebras can be Read Online from any device for your convenience.
Indecomposable Representations of Graphs and Algebras Book PDF Summary
I.N. Bernstein, I.M. Gelfand and V.A. Ponomarev have recently shown that the bijection, first observed by P. Gabriel, between the indecomposable representations of graphs ("quivers") with a positive definite quadratic form and the positive roots of this form can be proved directly. Appropriate functors produce all indecomposable representations from the simple ones in the same way as the canonical generators of the Weyl group produce all positive roots from the simple ones. This method is extended in two directions. In order to deal with all Dynkin diagrams rather than with those having single edges only, we consider valued graphs ("species"). In addition, we consider valued graphs with positive semi-definite quadratic form, i.e. extended Dynkin diagrams. The main result of the paper describes all indecomposable representations up to the homogeneous ones, of a valued graph with positive semi-definite quadratic form. These indecomposable representations are of two types: those of discrete dimension type, and those of continuous dimension type.
Detail Book of Indecomposable Representations of Graphs and Algebras PDF
- Author : Vlastimil Dlab
- Release : 20 September 1976
- Publisher : American Mathematical Soc.
- ISBN : 9780821818732
- Genre : Mathematics
- Total Page : 66 pages
- Language : English
- PDF File Size : 10,7 Mb
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