?Hall algebra of the projective line and ?-Onsager algebra
?Hall algebra of the projective line and ?-Onsager algebra
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?射影线的霍尔代数和?-Onsager 代数
DOI：
10.1090/tran/8798
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发表时间：
2023
影响因子：
1.3
通讯作者：
Wang, Weiqiang
中科院分区：
文献类型：
--
作者：
Lu, Ming;Ruan, Shiquan;Wang, Weiqiang
射影直线的Hall代数定义为射影直线上凝聚层的非周期复形范畴的扭曲半导子Ringel-Hall代数。这个霍尔代数在Drinfeld类型的表述中实现了泛Onsager代数(即分裂仿射类型的量子群)。众所周知，Kronecker箭图的霍尔代数在其Serre类型的表示中实现了相同的代数。然后，我们建立了诱导这两个Hall代数同构的导出等价，解释了在这两个表示下的-Onsager代数的同构。参考文献
TheHall algebra of the projective line is by definition the twisted semi-derived Ringel-Hall algebra of the category of-periodic complexes of coherent sheaves on the projective line. ThisHall algebra is shown to realize the universal-Onsager algebra (ie,quantum group of split affinetype) in its Drinfeld type presentation. TheHall 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 twoHall algebras, explaining the isomorphism of the-Onsager algebra under the two presentations. References