Tame prinjective type and Tits form of two-peak posets I

Abstract

The main aim of this paper is to give a simple criterion for a finite poset I with two maximal elements to have the category I-spr of socle projective representations of tame representation type. Our main result is Theorem 1 which asserts that for any upper chain reducible poset I with two maximal elements (see Definition 8) the category I-spr is of tame representation type if and only if the Tits quadratic form q I : Q I → Q (1.1) of I is weakly non-negative, or equivalently, if and only if I does not contain as a peak subposet any of the one-peak posets N 1 ∗,…, N 6 ∗ of Nazarova presented in Theorem 1 or any of the 41 two-peak posets listed in Table 1.