کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4603544 1336964 2008 12 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On the periodicity of Coxeter transformations and the non-negativity of their Euler forms
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
On the periodicity of Coxeter transformations and the non-negativity of their Euler forms
چکیده انگلیسی

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.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 428, Issue 4, 1 February 2008, Pages 742-753