Tokyo-Nagoya Algebra Seminar

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Organizer(s) Noriyuki Abe, Aaron Chan, Osamu Iyama, Yasuaki Gyoda, Hiroyuki Nakaoka, Ryo Takahashi

2023/10/12

10:30-12:00   Online
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 ]
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html