Vershik, A. M.; Kokhas’, K. P. Computation of the Grothendieck group of the algebra \(\mathbb{C}(PSL(2,k))\), where \(k\) is a countable algebraically closed field. (English. Russian original) Zbl 0746.16004 Leningr. Math. J. 2, No. 6, 1251-1259 (1991); translation from Algebra Anal. 2, No. 6, 98-106 (1990). Let \(F_ p\) be a prime finite field of characteristic \(p\), and \({\overline F}_ p\) its algebraic closure. Consider the countable group \(\Gamma=PSL(2,{\overline F}_ p))\) and its complex group algebra \({\mathbb{C}}(\Gamma)\). We give a complete description of the Grothendieck group of finitely generated projective modules over this algebra and the cone of faithful projective modules. Cited in 2 Documents MSC: 16E20 Grothendieck groups, \(K\)-theory, etc. 20G05 Representation theory for linear algebraic groups 19A31 \(K_0\) of group rings and orders 16D40 Free, projective, and flat modules and ideals in associative algebras 16S34 Group rings 20C32 Representations of infinite symmetric groups 20G40 Linear algebraic groups over finite fields 20C07 Group rings of infinite groups and their modules (group-theoretic aspects) Keywords:complex group algebra; Grothendieck group; finitely generated projective modules PDFBibTeX XMLCite \textit{A. M. Vershik} and \textit{K. P. Kokhas'}, Leningr. Math. J. 2, No. 6, 1251--1259 (1990; Zbl 0746.16004); translation from Algebra Anal. 2, No. 6, 98--106 (1990)