Tame Algebras and Generic Modules
Tame Algebras and Generic Modules
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DOI：
10.1112/plms/s3-63.2.241
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发表时间：
1991-09
影响因子：
1.8
通讯作者：
W. Crawley-Boevey
中科院分区：
文献类型：
--
作者：
W. Crawley-Boevey
设A是代数闭域k上的有限维代数（与1结合）。根据Drozd的Tame和Wild定理[4]可知，A是“Tame”的，因此不可分解的有限维A-模可以仅使用一个连续参数进行参数化，或者A是“Wild”的，并且它具有依赖于任意多个连续参数的不可分解模族。当然，这些定义需要精确，为了驯服，可以这样做：定义。如果对于所有的d ^ f^ J存在有限个AA^ A^-双模A/，，…， Mn，它们不受秩的右^[A^-模的约束，并且使得每一个维数为d的不可分解的A模都同构于Mt®k [X] k [X]/(X - A)，对于某些1= si = s n和Xek。
Let A be a finite-dimensional algebra (associative, with 1) over an algebraically closed field k. By Drozd's Tame and Wild Theorem [4] it is known that either A is' tame', so that the indecomposable finite-dimensional A-modules can be parametrized using only one continuous parameter, or A is' wild', and it has families of indecomposable modules depending on arbitrarily many continuous parameters. Of course these definitions need to be made precise, and for tameness it can be done as follows:DEFINITION. We say that A is of tame representation type if for all d ef^ J there are a finite number of AA^ A^-bimodules A/,,..., Mn which are free of rankd as right^[A^-modules, and such that every indecomposable A-module of dimension d is isomorphic to Mt® k [X] k [X]/(X—A) for some 1= s i= s n and Xek.