کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4587637 1334152 2008 39 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On Galois coverings and tilting modules
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
On Galois coverings and tilting modules
چکیده انگلیسی

Let A be a basic connected finite dimensional algebra over an algebraically closed field k. Let T be a basic tilting A-module with arbitrary finite projective dimension. For a fixed group G we compare the set of isoclasses of connected Galois coverings of A with group G and the set of isoclasses of connected Galois coverings of EndA(T) with group G. Using the Hasse diagram (see [D. Happel, L. Unger, On a partial order of tilting modules, Algebr. Represent. Theory 8 (2) (2005) 147–156] and [C. Riedtmann, A. Schofield, On a simplicial complex associated with tilting modules, Comment. Math. Helv. 66 (1) (1991) 70–78]) of basic tilting A-modules, we give sufficient conditions on T under which there is a bijection between these two sets (these conditions are always verified when A is of finite representation type). Then we apply these results to study when the simple connectedness of A implies the one of EndA(T) (see [I. Assem, E.N. Marcos, J.A. de la Peña, The simple connectedness of a tame tilted algebra, J. Algebra 237 (2) (2001) 647–656]). Finally, using an argument due to W. Crawley-Boevey, we prove that the type of any simply connected tilted algebra is a tree and that its first Hochschild cohomology group vanishes.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Algebra - Volume 319, Issue 12, 15 June 2008, Pages 4961-4999