KBSM of lens spaces L(p,2) and L(4k,2k + 1)

J. Hoste and J. H. Przytycki computed the Kauffman bracket skein module (KBSM) of lens spaces in their papers published in 1993 and 1995. By using a basis for the KBSM of a fibered torus, we construct new bases for the KBSMs of two families of lens spaces: [Formula: see text] and [Formula: see text] with [Formula: see text]. For KBSM of [Formula: see text], we find a new generating set that yields its decomposition into a direct sum of cyclic modules.