- Hall polynomials for the representation-finite hereditary algebras.
Adv. Math. 84 (1990), 137-178
The Hall polynomial φ11 is T(T3-2T2-T+3) as calculated on page 171.
- Preprint: Morphisms determined by objects: The case of modules over artin algebras
The remark after Lemma 2 has to be corrected. Let L be
an indecomposable summand L of the kernel K of a map f:X -> Y. It is
possible that the composition of the embeddings L -> K -> X is non-split,
whereas L is not a summand of an intrinsic kernel of f.
As an example, take the quiver o <- o <- o,
take X = (kkk)\oplus (0k0), Y = (00k) and f the canonical
projection. Then the kernel K is (kk0)\oplus (0k0), the intrinsic kernel
is (kk0)\oplus (000) (there is just one). The kernel has also a direct
decomposition L\oplus (0k0) with L \neq (kk0), say L being generated by the element
(0,(1,1),0) in (kk0)\oplus (0k0). Then the composition
of the embeddings L -> K -> X is not a split monomorphism,
but L is not a direct summand of any intinsic kernel.
Claus Michael Ringel
Last modified: Wed Jul 15 09:58:22 CEST 2009