题目: A class of quadratic matrix equations over finite fields
Tencent会议： ID：710 573 342
摘要: The present talk contains some interesting thoughts of algebra, geometry, and separating invariants, especially focusing on solutions to the parameter-independent Yang-Baxter matrix equation over a finite field. For a special case, we present an elementary approach from Linear Algebra and Abstract Algebra to calculate the cardinality of all solutions to the equation. We consider the conjugation action of the general linear group on the set of all solutions and obtain the number of all orbits. We show that the classical conjugation invariants separate these orbits and find the vanishing ideal of these orbits. This talk is based on a joint work (arXiv:2008.12457) with Xinxin Zhang, and I believe that the techniques involved in this talk will be friendly to graduate students.