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Math 7290 Fall 2009 Finite-Dimensional Algebras P. Achar

Summary: Math 7290 Fall 2009
Finite-Dimensional Algebras P. Achar
Problem Set 3
Due: October 29, 2009
1. Auslander≠Reiten≠SmalÝ, Chapter 3, Exercise 2.
2. Auslander≠Reiten≠SmalÝ, Chapter 3, Exercise 6.
3. Auslander≠Reiten≠SmalÝ, Chapter 3, Exercise 7.
The exercises in Chapter 3 have lots of other specific examples of quivers with various properties. It
might be interesting to look through the problems even if you don't end up working on any of them.
4. Auslander≠Reiten≠SmalÝ, Chapter 4, Exercise 3.
5. Let (, ) denote the following quiver with relations:


ee = 0
(a) Determine the isomorphism classes of indecomposable representations of (, ). (There are five:
2 simple objects; 2 indecomposable projectives that happen to also be injective; and one other
that is neither projective nor injective.)


Source: Achar, Pramod - Department of Mathematics, Louisiana State University


Collections: Mathematics