A criterion for tame prinjective type for a class of posets with zero-relations is given in terms of the associated prinjective Tits quadratic form and a list of hypercritical posets. A consequence of this result is that if is a three-partite subamalgam of a tiled order then it is of tame lattice type if and only if the reduced Tits quadratic form associated with in [26] is weakly non-negative. The result generalizes a criterion for tameness of such orders given by Simson [28] and gives an affirmative answer to [28, Question 4.7].
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm91-1-4,
author = {Stanis\l aw Kasjan},
title = {Tameness criterion for posets with zero-relations and three-partite subamalgams of tiled orders},
journal = {Colloquium Mathematicae},
volume = {91},
year = {2002},
pages = {39-68},
zbl = {1056.16010},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm91-1-4}
}
Stanisław Kasjan. Tameness criterion for posets with zero-relations and three-partite subamalgams of tiled orders. Colloquium Mathematicae, Tome 91 (2002) pp. 39-68. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm91-1-4/