تقرير
Dimensions of $\tau$-tilting modules over path algebras and preprojective algebras of Dynkin type
| العنوان: | Dimensions of $\tau$-tilting modules over path algebras and preprojective algebras of Dynkin type |
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| المؤلفون: | Aoki, Toshitaka, Mizuno, Yuya |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Representation Theory, Mathematics - Combinatorics, Mathematics - Rings and Algebras |
| الوصف: | In this paper, we introduce a new generating function called $d$-polynomial for the dimensions of $\tau$-tilting modules over a given finite dimensional algebra. Firstly, we study basic properties of $d$-polynomials and show that it can be realized as a certain sum of the $f$-polynomials of the simplicial complexes arising from $\tau$-rigid pairs. Secondly, we give explicit formulas of $d$-polynomials for preprojective algebras and path algebras of Dynkin quivers by using a close relation with $W$-Eulerian polynomials and $W$-Narayana polynomials. Thirdly, we consider the ordinary and exponential generating functions defined from $d$-polynomials and give closed-form expressions in the case of preprojective algebras and path algebras of Dynkin type $\mathbb{A}$. Comment: 34 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2402.13527 |
| رقم الأكسشن: | edsarx.2402.13527 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |