Computing Almost Split Sequences: An algorithm for computing almost split sequences of finitely generated modules over a finite dimensional algebra

Abstract

An artin algebra $l$ over a commutative, local, artinian ring $R$ was fixed, and with this foundation some topics from representation theory were discussed. A series of functors of module categories were defined, and almost split sequences were introduced with some basic results. An isomorphism $omega_{delta,X} : D delta^* rightarrow delta_*(DTr(X))$ of $Gamma$-modules for an artin $R$-algebra $Gamma$ was constructed. The isomorphism $omega_{delta,X}$ was applied to a special case, yielding a deterministic algorithm for computing almost split sequences in the case that $R$ is a field.