The alternating central extension U^+_q of U^+_q is isomorphic to U^+_q tensor F[z1,z2,...] via a surjective homomorphism sending alternating generators to alternating elements, with those generators forming a PBW basis.
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The alternating central extension for the positive part of $U_q(\widehat{\mathfrak{sl}}_2)$
The alternating central extension U^+_q of U^+_q is isomorphic to U^+_q tensor F[z1,z2,...] via a surjective homomorphism sending alternating generators to alternating elements, with those generators forming a PBW basis.