摘  要： This is joint work with Ming Lu and Weiqiang Wang. The i-Hall algebra of the projective line is by definition the twisted semi-derived Ringel-Hall algebra of the category of 1-periodic complexes of coherent sheaves on the projective line. This i-Hall algebra is shown to realize the universal q-Onsager algebra (i.e., i-quantum group of split affine sl_2 type) in its Drinfeld type presentation. The i-Hall algebra of the Kronecker quiver was known earlier to realize the same algebra in its Serre type presentation. We then establish a derived equivalence which induces an isomorphism of these two i-Hall algebras, explaining the isomorphism of the q-Onsager algebra under the two presentations.

报告人简介：阮诗佺，厦门大学副教授，2014年博士毕业于厦门大学，2014-2017年清华大学丘成桐数学科学中心博士后。科研方向主要是利用加权射影直线的凝聚层范畴及其导出范畴的结构，研究它们的倾斜理论以及Hall代数结构，并建立它们与其它数学分支的联系。目前在Int. Math. Res. Not., Math. Z.，J. Algebra, J. Pure Appl. Algebra等期刊发表高水平论文十余篇。

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