Non-isomorphic Derived-Equivalent Tubular Curves and Their Associated Tubular Algebras
Non-isomorphic Derived-Equivalent Tubular Curves and Their Associated Tubular Algebras
复制标题
非同构导出等效管状曲线及其相关管状代数
DOI：
10.1006/jabr.1999.8200
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发表时间：
2000
影响因子：
0.9
通讯作者：
D. Kussin
中科院分区：
文献类型：
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作者：
D. Kussin
设R是真实的数域。构造了两个管标准R -代数（在C. M. Ringel/W. Crawley-Boevey（1990），《代数主题》（Topics in Algebra），Banach Center Publ. No. 26，pp. 407-432）），它们既不是同构的，也不是对偶的，而是倾斜等价的。这涉及到这样一个事实，即每个这些代数承认两个不同的同构类的标准稳定管分离管家庭。这些结果是由存在两条非同构的管状例外曲线（H。伦辛（1998年，在“环理论的趋势”（V. Dlab等人，Eds.），CMS会议程序，Vol. 22，pp. 71-97，Am.数学会，普罗维登斯）在R上导出等价，一个具有可交换函数域，另一个具有非可交换函数域。此外，我们分类的所有一般模在这样的管状代数。
Abstract Let R be the field of real numbers. We construct two tubular canonical R -algebras (in the sense of C. M. Ringel/W. Crawley–Boevey (1990, in “Topics in Algebra,” Banach Center Publ. No. 26, pp. 407–432)) which are neither isomorphic nor dual to each other, but which are tilting-equivalent. This relates to the fact that each of these algebras admits two distinct isomorphism classes of separating tubular families of standard stable tubes. The results are derived from the existence of two non-isomorphic tubular exceptional curves (in the sense of H. Lenzing (1998, in “Trends in Ring Theory” (V. Dlab et al., Eds.), CMS Conf. Proc., Vol. 22, pp. 71–97, Am. Math. Soc., Providence)) over R which are derived-equivalent, one having a commutative and the other a non-commutative function field. Furthermore, we classify all generic modules over such tubular algebras.