Wild tilted algebras revisited

Otto Kerner
1997 Colloquium Mathematicum  
In this paper wild tilted algebras are studied. Following [6] an algebra B is called tilted (of type A) if there exists a finite-dimensional hereditary algebra A over some field k and a tilting module T in the category A-mod of finite-dimensional left A-modules with B = End A (T ). The tilting module T has a structure as an (A, B)-bimodule and induces in B-mod a splitting torsion pair (X , Y), where the torsion-free class Y is the full subcategory of B-mod, defined by the objects M with Tor 1 B
more » ... ects M with Tor 1 B (T, M ) = 0, whereas the torsion class X is defined by the objects N with T ⊗ B N = 0. A tilted algebra B of type A is only wild if A is wild hereditary. It was shown in [9] that the study of Y (respectively, X ) can be reduced to the case of tilting modules without nonzero direct summands in the preinjective component I(A) (respectively, preprojective component P(A)).
doi:10.4064/cm-73-1-67-81 fatcat:uv62gzdqnfeahn3ytfziqyerre