 
Summary: TRUNCATED PATH ALGEBRAS ARE
HOMOLOGICALLY TRANSPARENT
A. Dugas, B. HuisgenZimmermann, and J. Learned
To the memory of Tony Corner
1. Introduction and notation
The problem of opening up general access roads to the finitistic dimensions of a finite
dimensional algebra , given through quiver and relations, is quite challenging. This is
witnessed, for instance, by the fact that the longstanding question "Is the (left) little
finitistic dimension of ,
fin dim = sup{p dim M  M P<
(mod)},
always finite?" (Bass 1960) has still not been settled. Here p dim M is the projective
dimension of a module M, and P<
(mod) denotes the category of finitely generated
(left) modules of finite projective dimension.
In [1], Babson, the second author, and Thomas showed that truncated path algebras of
quivers are particularly amenable to geometric exploration, while nonetheless displaying
a wide range of interesting phenomena. This led the authors of the present paper to the
serendipitous discovery that the same is true for the homology of such algebras. By a
truncated path algebra we mean an algebra of the form KQ/I, where KQ is the path
