报告题目：Poisson structure and second quantization of quantum cluster algebras

报 告 人：李方教授（浙江大学）

报告时间：2020年12月7日 15:00

报告地点：数统院5楼数学研究中心

报告摘要：

Motivated by the phenomenon that compatible Poisson structures on a cluster algebra play a key role on its quantization (that is, quantum cluster algebra), we introduce the second quantization of a quantum cluster algebra, which means the correspondence between compatible Poisson structures of the quantum cluster algebra and its secondly quantized cluster algebras. Based on this observation, we find that a quantum cluster algebra possesses dual quantum cluster algebras such that their second quantization is essentially the same.

As an example, we give the secondly quantized cluster algebra A_{p,q}(SL(2)) of Fun_{\C}(SL_{q}(2)) and show that it is a non-trivial second quantization, which may be realized as a parallel supplement to two parameters quantization of the general quantum group. Furthermore, we obtain a class of quantum cluster algebras with coefficients which possess a non-trivial second quantization. Its one special kind is quantum cluster algebras with almost principal coefficients with an additional condition.

Finally, we prove that the compatible Poisson structures of a quantum cluster algebra without coefficients is always a locally standard Poisson structure. Following this, it is shown that the second quantization of a quantum cluster algebra without coefficients is in fact trivial.

报告人简介：

李方，浙江大学教授，博士生导师，高等数学研究所所长，中国数学会理事。2000年至今已培养出22位博士生，有的已成为国内有一定学术影响的青年学者。在Adv. Math., J. Algebra等国内外重要期刊杂志上发表论文130余篇。先后主持国家自然科学基金6项和浙江省自然科学基金重大和重点项目各1项。曾获浙江省高校科技进步一等奖等奖项，是国家教育部新世纪人才和浙江省151人才入选者。