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Published in:
2015 | OriginalPaper | Chapter
3. Algebras
Author : Michael Barot
Published in: Introduction to the Representation Theory of Algebras
Publisher: Springer International Publishing
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Abstract
Representations of quivers is a modern language which now will be connected to the classic one of modules over an algebra. This translation will take up the whole chapter. With this three different languages are developed for the same thing, each of which with a distinctive flavour. All three languages have their own advantages and it is convenient to be able to switch freely between them as in the literature all three of them are used.
As we will see, it is quite easy to associate an algebra to a quiver, but the converse is rather more demanding and requires the development of certain concepts: some elements of an algebra called “idempotents” and others “radicals”. This are concepts, which also in the language of categories and functors play an important role.