Tameness criterion for posets with zero-relations and three-partite subamalgams of tiled orders

Stanisław Kasjan¹

¹ Faculty of Mathematics and Computer Science Nicholas Copernicus University Chopina 12/18 87-100 Toruń, Poland

Colloquium Mathematicum, Tome 91 (2002) no. 1, pp. 39-68.

Résumé

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 ${\mit\Lambda }^{\bullet }$ 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 ${\bf q}_{{\mit\Lambda }^{\bullet }}$ associated with ${\mit\Lambda }^{\bullet }$ 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].

Détail

DOI : 10.4064/cm91-1-4

Keywords: criterion tame prinjective type class posets zero relations given terms associated prinjective tits quadratic form list hypercritical posets consequence result mit lambda bullet three partite subamalgam tiled order tame lattice type only reduced tits quadratic form mit lambda bullet associated mit lambda bullet weakly non negative result generalizes criterion tameness orders given simson gives affirmative answer question