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

Stanisław Kasjan

Colloquium Mathematicae (2002)

  • Volume: 91, Issue: 1, page 39-68
  • ISSN: 0010-1354

Abstract

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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 Λ • 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 q Λ • associated with Λ • 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].

How to cite

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Stanisław Kasjan. "Tameness criterion for posets with zero-relations and three-partite subamalgams of tiled orders." Colloquium Mathematicae 91.1 (2002): 39-68. <http://eudml.org/doc/284250>.

@article{StanisławKasjan2002,
abstract = {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 $Λ^\{•\}$ 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 $q_\{Λ^\{•\}\}$ associated with $Λ^\{•\}$ 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].},
author = {Stanisław Kasjan},
journal = {Colloquium Mathematicae},
keywords = {tame prinjective type; Tits quadratic forms; hypercritical posets; tiled orders; tame lattice type; tame representation type },
language = {eng},
number = {1},
pages = {39-68},
title = {Tameness criterion for posets with zero-relations and three-partite subamalgams of tiled orders},
url = {http://eudml.org/doc/284250},
volume = {91},
year = {2002},
}

TY - JOUR
AU - Stanisław Kasjan
TI - Tameness criterion for posets with zero-relations and three-partite subamalgams of tiled orders
JO - Colloquium Mathematicae
PY - 2002
VL - 91
IS - 1
SP - 39
EP - 68
AB - 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 $Λ^{•}$ 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 $q_{Λ^{•}}$ associated with $Λ^{•}$ 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].
LA - eng
KW - tame prinjective type; Tits quadratic forms; hypercritical posets; tiled orders; tame lattice type; tame representation type
UR - http://eudml.org/doc/284250
ER -

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