ALGEBRAS WHOSE TITS FORM ACCEPTS A MAXIMAL OMNIPRESENT ROOT

作者：de la Pena Jose A^*; Skowronski Andrzej

来源：Transactions of the American Mathematical Society, 2014, 366(1): 395-417.

• Root of the Tits form
• weakly non-negative quadratic form
• maximal omnipresent root
• tilted algebra
• tame algebra
• exceptional index

Let k be an algebraically closed field and A be a finite-dimensional associative basic k-algebra of the form A = kQ/I where Q is a quiver without oriented cycles or double arrows and I is an admissible ideal of kQ. We consider roots of the Tits form q(A), in particular in the case where q(A) is weakly non-negative. We prove that for any maximal omnipresent root v of q(A), there exists an indecomposable A-module X such that v=dim X. Moreover, if A is strongly simply connected, the existence of a maximal omnipresent root of q(A) implies that A is tame of tilted type.

• 出版日期2014-1