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EXT-FINITE MODULES FOR WEAKLY SYMMETRIC ALGEBRAS WITH RADICAL CUBE ZERO
- Part of
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- Journal:
- Journal of the Australian Mathematical Society / Volume 102 / Issue 1 / February 2017
- Published online by Cambridge University Press:
- 19 September 2016, pp. 108-121
- Print publication:
- February 2017
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- Article
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Assume that
$A$ is a finite-dimensional algebra over some field, and assume that 
$A$ is weakly symmetric and indecomposable, with radical cube zero and radical square nonzero. We show that such an algebra of wild representation type does not have a nonprojective module 
$M$ whose ext-algebra is finite dimensional. This gives a complete classification of weakly symmetric indecomposable algebras which have a nonprojective module whose ext-algebra is finite dimensional. This shows in particular that existence of ext-finite nonprojective modules is not equivalent with the failure of the finite generation condition (Fg), which ensures that modules have support varieties.
