Assume that k is a field of characteristic different from 2. We show that if Γ is a strongly simply connected k-algebra of non-polynomial growth, then there exists a special family of pointed Γ-modules, called an independent pair of dense chains of pointed modules. Then it follows by a result of Ziegler that Γ admits a super-decomposable pure-injective module if k is a countable field.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm136-2-3,
author = {Stanis\l aw Kasjan and Grzegorz Pastuszak},
title = {On the existence of super-decomposable pure-injective modules over strongly simply connected algebras of non-polynomial growth},
journal = {Colloquium Mathematicae},
volume = {135},
year = {2014},
pages = {179-220},
zbl = {1322.16009},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm136-2-3}
}
Stanisław Kasjan; Grzegorz Pastuszak. On the existence of super-decomposable pure-injective modules over strongly simply connected algebras of non-polynomial growth. Colloquium Mathematicae, Tome 135 (2014) pp. 179-220. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm136-2-3/