تقرير
$\tau$-tilting theory and silting theory of skew group algebra extensions
| العنوان: | $\tau$-tilting theory and silting theory of skew group algebra extensions |
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| المؤلفون: | Kimura, Yuta, Koshio, Ryotaro, Kozakai, Yuta, Minamoto, Hiroyuki, Mizuno, Yuya |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Representation Theory |
| الوصف: | Let $\Lambda$ be a finite dimensional algebra with an action by a finite group $G$ and $A:= \Lambda *G$ the skew group algebra. One of our main results asserts that the canonical restriction-induction adjoint pair of the skew group algebra extension $\Lambda \subset A$ induces a poset isomorphism between the poset of $G$-stable support $\tau$-tilting modules over $\Lambda$ and that of $(\!\!\!\mod G)$-stable support $\tau$-tilting modules over $A$. We also establish a similar poset isomorphism of posets of appropriate classes of silting complexes over $\Lambda$ and $A$. These two results generalize and unify preceding results by Huang-Zhang, Breaz-Marcus-Modoi and the second and the third authors. Moreover, we give a practical condition under which $\tau$-tilting finiteness and silting discreteness of $\Lambda$ are inherited to those of $A$. As applications we study $\tau$-tilting theory and silting theory of the (generalized) preprojective algebras and the folded mesh algebras. Among other things, we determine the posets of support $\tau$-tilting modules and of silting complexes over preprojective algebra $\Pi(\Bbb{L}_{n})$ of type $\Bbb{L}_{n}$. Comment: 2nd version: minor corrections |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2407.06711 |
| رقم الأكسشن: | edsarx.2407.06711 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |