Representations of U¯qsℓ(2|1) at even roots of unity

Source abstract

We construct all projective modules of the restricted quantum group U¯qsℓ(2|1) at an even, 2p th, root of unity. This 64p4-dimensional Hopf algebra is a common double bosonization of two rank-2 Nichols algebras 𝔅(X) with fermionic generator(s). We show that the category of U¯qsℓ(2|1)-modules is equivalent to the category of Yetter–Drinfeld 𝔅(X)-modules in Cρ=HHY\kern -1ptD for H = ℤ2p ⊗ ℤ2p, where the coaction is defined by a universal R-matrix ρ ∈ H ⊗ H. As an application of the projective module construction, we study the basic algebra of U¯qsℓ(2|1) and find the associative algebra structure and the dimension, 5p2 − p + 4, of its center.