The Alternating Central Extension of the q-Onsager Algebra

The $q$-Onsager algebra $O_q$ is presented by two generators $W_0$, $W_1$ and relations, called the $q$-Dolan/Grady relations. Recently Baseilhac Koizumi introduced a current $\mathcal A_q$ for $O_q$. Soon afterwards, Shigechi gave presentation of We show that these give PBW basis A_q$. Using this basis, we isomorphic to $O_q \otimes \mathbb F \lbrack z_1, z_2, \ldots \rbrack$, where $\mathbb F$ ground field $\lbrace z_n \rbrace_{n=1}^\infty $ are mutually commuting indeterminates. Recall positive part $U^+_q$ quantized enveloping $U_q(\widehat{\mathfrak{sl}}_2)$. Our results related in same way alternating central extension $U^+_q$. For reason, propose call