Mathematical Sciences: Representation Theory of Algebras

这项研究涉及到代数的表示理论。主要研究者将通过检验某些正合列与一个模到另一个模的同态之间的关系来检验这类Artin代数的同调性质。此外，还将研究Artin环上模的射影分解的结构。证明了代数闭域上的有限维Artin代数上的任意有限生成单模的分解可以通过算法得到。这种方法将扩展到更一般的情况。

This research is concerned with the representation theory of algebras. The principal investigator will examine the homological properties of the class of Artin algebras by examining the relationship between certain exact sequences and the homomorphisms of one module into another. In addition, the structure of projective resolutions of modules over Artinian rings will be studied. It has been shown that a resolution for an arbitrary finitely generated simple module over an Artin algebra, finite dimensional over an algegraically closed field, can be obtained algorithmically. This approach will be extended to more general situations.