L-FUNCTORS AND ALMOST SPLIT SEQUENCES.

L-functors (Rump, 2001) provide a new tool for the study of Auslander--Reiten quivers associated with an isolated singularity in the sense of M. Auslander. We show that L-functors L, L- : M → M admit an intrinsic definition for an arbitrary additive category M. When they exist, they endow M with a structure closely related to that of a triangulated category. If M is the homotopy category M(&scriptA; ) of two-termed complexes over an additive category &scriptA;, we establish a one-to-one correspondence between L-functors on M(&scriptA;) and classes of short exact sequences in &scriptA; which make &scriptA; into an exact category with almost split sequences. This applies, in particular, to categories, &scriptA; = Λ-CM of Cohen--Macaulay modules over a Cohen--Macaulay R-order Λ for arbitrary dimension of R. [ABSTRACT FROM AUTHOR]