Globular cluster stars show chemical abundance patterns typical of hot-CNO processing. Lithium is easily destroyed by proton capture in stellar environments, so its abundance may be crucial to discriminate among different models proposed to account for multiple populations. In order to reproduce the observed O-Na anticorrelation and other patterns typical of multiple populations, the formation of second generation stars must occur from the nuclearly processed stellar ejecta, responsible of the chemical anomalies, diluted with pristine gas having the composition of first generation stars. The lithium abundance in the unprocessed gas -which is very likely to be equal to the lithium abundance emerging from the Big Bang- affects the lithium chemical patterns among the cluster stars. This paper focuses on a scenario in which processed gas is provided by asymptotic giant branch (AGB) stars. We examine the predictions of this scenario for the lithium abundances of multiple populations. We study the role of the non-negligible lithium abundance in the ejecta of massive AGB (A(Li)~2), and, at the same time, we explore how our models can constrain the extremely large ---and very model dependent--- lithium yields predicted by recent super--AGB models. We show that the super--AGB yields may be tested by examining the lithium abundances in a large set of blue main sequence stars in wCen and/or NGC2808. In addition, we examine the different model results obtained by assuming for the pristine gas either the Big Bang abundance predicted by the standard models (A(Li)=2.6-2.7), or the abundance detected at the surface of population II stars (A(Li)=2.2-2.3). Once a chemical model is well constrained, the O--Li distribution could perhaps be used to shed light on the primordial lithium abundance.
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