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Title:听The alternating central extension of the $q$-Onsager algebra.

础产蝉迟谤补肠迟:听The $q$-Onsager algebra $O_q$ is a quantized enveloping algebra for the Onsager Lie algebra $O$. Recently Baseilhac, Koizumi, and Shigechi introduced an algebra $mathcal O_q$ called the alternating central extension of $O_q$. In this talk, our goal is to describe how $O_q$ is related to $mathcal O_q$. To motivate this description, we first consider a toy model, involving the positive part $U^+_q$ of $U_q(widehat{mathfrak{sl}}_2)$ and its alternating central extension $mathcal U^+_q$. We will see that $O_q$ is related to $mathcal O_q$ in essentially the same way as $U^+_q$ is related to $mathcal U^+_q$.听We finish with an open problem.

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