The Projective Class Rings of Bosonizations of Quantum Linear Spaces

In this article, we study the projective class ring of bosonization [Formula: see text] of quantum linear space [Formula: see text]. We classify all finite-dimensional indecomposable projective [Formula: see text]-modules and simple [Formula: see text]-modules. The decomposition rules for tensor products of indecomposable projective [Formula: see text]-modules and simple [Formula: see text]-modules are given, and the structures of projective class ring [Formula: see text] are described. It turns out that [Formula: see text] is a commutative ring generated by [Formula: see text] elements subject to certain relations. Finally, we classify all finite-dimensional indecomposable modules over the complexified projective class ring[Formula: see text].