Algebras of generalized quaternion type
Algebras of generalized quaternion type
复制标题
广义四元数类型的代数
DOI：
10.1016/j.aim.2019.04.037
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发表时间：
2017
影响因子：
1.7
通讯作者：
Andrzej Skowro'nski
中科院分区：
文献类型：
--
作者：
K. Erdmann;Andrzej Skowro'nski
We introduce and study the algebras of generalized quaternion type, being natural generalizations of algebras which occurred in the study of blocks of group algebras with generalized quaternion defect groups. We prove that all these algebras, with 2-regular Gabriel quivers, are periodic algebras of period 4 and very specific deformations of the weighted surface algebras of triangulated surfaces with arbitrarily oriented triangles. The main result of the paper forms an important step towards the Morita equivalence classification of all periodic symmetric tame algebras of non-polynomial growth. Applying the main result, we establish existence of wild periodic algebras of period 4, with arbitrary large number (at least 4) of pairwise non-isomorphic simple modules. These wild periodic algebras arise as stable endomorphism rings of cluster tilting Cohen-Macaulay modules over one-dimensional hypersurface singularities.
