论文标题
$ \ imath $投影线的霍尔代数和$ Q $ -ONSAGER代数
$\imath$Hall algebra of the projective line and $q$-Onsager algebra
论文作者
论文摘要
从定义上讲，投影线的$ \ imath $ hall代数是$ 1 $ $ 1 $ - 周期性的林格 - 林格尔代数的扭曲，$ 1 $ - 周期性的连贯的滑轮上的综合滑轮上的复合体。该$ \ imath $ hall代数被证明可以意识到其Drinfeld类型的表达式中的通用$ Q $ -ONSAGER代数（即$ \ imath $量子组的分裂载体$ a_1 $ type）。 The $\imath$Hall algebra of the Kronecker quiver was known earlier to realize the same algebra in its Serre type presentation.然后，我们建立了一个派生的等效性，该等效性诱导了这两个$ \ imath $ hall代数的同构，并在两个演讲下解释了$ q $ ossager代数的同构。
The $\imath$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 $\imath$Hall algebra is shown to realize the universal $q$-Onsager algebra (i.e., $\imath$quantum group of split affine $A_1$ type) in its Drinfeld type presentation. The $\imath$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 $\imath$Hall algebras, explaining the isomorphism of the $q$-Onsager algebra under the two presentations.
