Article ID Journal Published Year Pages File Type
4603544 Linear Algebra and its Applications 2008 12 Pages PDF
Abstract

We show that for piecewise hereditary algebras, the periodicity of the Coxeter transformation implies the non-negativity of the Euler form. Contrary to previous assumptions, the condition of piecewise heredity cannot be omitted, even for triangular algebras, as demonstrated by incidence algebras of posets.We also give a simple, direct proof, that certain products of reflections, defined for any square matrix A with 2 on its main diagonal, and in particular the Coxeter transformation corresponding to a generalized Cartan matrix, can be expressed as , where A+, A- are closely associated with the upper and lower triangular parts of A.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory