## Tokyo-Nagoya Algebra Seminar

Seminar information archive ～02/26｜Next seminar｜Future seminars 02/27～

Organizer(s) | Noriyuki Abe, Aaron Chan, Osamu Iyama, Yasuaki Gyoda, Hiroyuki Nakaoka, Ryo Takahashi |
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### 2023/10/12

10:30-12:00 Online

q-deformed rational numbers, Farey sum and a 2-Calabi-Yau category of A_2 quiver (English)

http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html

**Xin Ren**(Kansai University)q-deformed rational numbers, Farey sum and a 2-Calabi-Yau category of A_2 quiver (English)

[ Abstract ]

Let q be a positive real number. The left and right q-deformed rational numbers were introduced by Bapat, Becker and Licata via regular continued fractions, and the right q-deformed rational number is exactly q-deformed rational number considered by Morier-Genoud and Ovsienko, when q is a formal parameter. They gave a homological interpretation for left and right q-deformed rational numbers by considering a special 2-Calabi–Yau category associated to the A_2 quiver.

In this talk, we begin by introducing the above definitions and related results. Then we give a formula for computing the q-deformed Farey sum of the left q-deformed rational numbers based on the negative continued fractions. We combine the homological interpretation of the left and right q-deformed rational numbers and the q-deformed Farey sum, and give a homological interpretation of the q-deformed Farey sum. We also apply the above results to real quadratic irrational numbers with periodic type.

[ Reference URL ]Let q be a positive real number. The left and right q-deformed rational numbers were introduced by Bapat, Becker and Licata via regular continued fractions, and the right q-deformed rational number is exactly q-deformed rational number considered by Morier-Genoud and Ovsienko, when q is a formal parameter. They gave a homological interpretation for left and right q-deformed rational numbers by considering a special 2-Calabi–Yau category associated to the A_2 quiver.

In this talk, we begin by introducing the above definitions and related results. Then we give a formula for computing the q-deformed Farey sum of the left q-deformed rational numbers based on the negative continued fractions. We combine the homological interpretation of the left and right q-deformed rational numbers and the q-deformed Farey sum, and give a homological interpretation of the q-deformed Farey sum. We also apply the above results to real quadratic irrational numbers with periodic type.

http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html