Returning Arrows for Self-injective Algebras and Artin-Schelter Regular Algebras
Returning Arrows for Self-injective Algebras and Artin-Schelter Regular Algebras
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DOI：
10.1016/j.jalgebra.2013.07.036
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发表时间：
2010-12
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影响因子：
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通讯作者：
J. Guo;Z. Can;Ying Yin
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文献类型：
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作者：
J. Guo;Z. Can;Ying Yin
我们证明，当为分级自射代数构造扭曲的平凡扩张时，返回箭头出现在箭袋中，同时在 Koszul 情况下复杂性增加一，并且在某些附加条件下表示维数也增加一。我们将我们的结果应用到Koszul Artin-Schelter正则代数上，得到了Koszul Artin-Schelter正则代数的一个推广族，其中一个是中心推广，一个是Calabi-Yau。
We show that when constructing twisted trivial extensions for a graded self-injective algebra, the returning arrows appear in the quiver, and in the meantime the complexity increases by one in Koszul cases, and the representation dimension also increases by one under certain additional conditions. We apply our results to Koszul Artin–Schelter regular algebras and obtain a family of extensions of a Koszul Artin–Schelter regular algebra, among them one is central extension and one is Calabi–Yau.