Projective class ring of a restricted quantum group $ \overline{U}_{q}(\mathfrak{sl}^{*}_2) $

Abstract

<abstract><p>In this paper, we compute the projective class ring of the new type restricted quantum group $ \overline{U}_{q}(\mathfrak{sl}^{*}_2) $. First, we describe the principal indecomposable projective $ \overline{U}_{q}(\mathfrak{sl}^{*}_2) $-modules and study their radicals, composition series, Cartan matrix of $ \overline{U}_{q}(\mathfrak{sl}^{*}_2) $ and so on. Then, we deconstruct the tensor products between two simple modules, two indecomposable projective modules and a simple module and an indecomposable projective module, into direct sum of some indecomposable representations. At last, we characterize the projective class ring by generators and relations explicitly.</p></abstract>