This is the first time I post a question on MO, so I'm shy a liite bit. Can you give a "non-trivial" example of a finite dimensional hereditary algebra which is quotient of an infinite dimensional algebra ?
By "non-trivial" I mean not by killing loops in the path algebra of some quiver, for example 
$k[X\_1] \times\ldots \times k[X\_n]/((X\_1)\times\ldots\times (X\_n))$.



Hereditary algebras as quotient algebras
If you use generators and relations, then any algebra is a quotient of an infinite-dimensional algebra, i.e., a quotient of the free associative algebra corresponding to the generators you pick.


