Investigation of algebras of infinite representation type

我们研究了域上有限维代数条的表示。特别是，我们与A.Skowronski和首席研究员共同研究了基于基座形变理论的自射代数(即Frobenius代数)。我们得到了以下三个主要结果：1.我们研究了一个名为‘ZA_∽问题’的公开问题，它指出一个含有ZA_∽类型AR-分支的代数是野的。我们证明了一个定理，作为推论，它蕴含了许多已知的代数有Za_∽-AR分支的充分条件。特别地，在代数没有恒等式的情况下，我们找到了问题的反例。利用有限维代数确定了重复代数的刚性自同构群的一种结构。研究了自射代数的模范畴，证明了稳定等价于由重复代数覆盖Galois的代数B的自内射代数A也有由重复代数覆盖的Galois覆盖.此外，我们还确定了至少有三个广义标准分支的代数和欧几里得类型的代数。

We studied representations of finite dimensional algebars over a field. In particular, we concentrated on the research of selfinjective algebas (ie Frobenius algebras) based on the theory of socle deformation studied by the joint work with A. Skowronski and the head investigator. We got the following three main results.1. We studied about the open problem called 'ZA_∽ problem' which states that an algebra with AR-components of ZA_∽ type is wild. We proved a therem which implies, as corollaries, many known sufficient conditions for algebras to have AR-components of ZA_∽ type. In particular, in the case when an algebra has no identity, we found a counterexample of the problem.2. We determined a structure of the rigid automorphism group of the repetitive algebras by finite dimensional algebras.3. We studied the module categories of selfinjecitve algebras, and we proved that a selfinjective algebra A stably equivalent to an algebra B with Galois covering by a repetitive algbra has also a Galois covering by a repetitive algebra. Moreover, we determined algebras with at least three generalized standared components, and algebras of Euclidean type.