Publication Date:
23 March 2020
Journal:
Journal of Knot Theory and Its Ramifications
Last Updated:
2020-12-30T06:32:56.69+00:00
Issue:
04
Volume:
29
DOI:
10.1142/s0218216520500182
page:
2050018-2050018
abstract:
The category of finite dimensional modules over the quantum superalgebra Uq𝔰𝔩(2|1) is not semi-simple and the quantum dimension of a generic Uq𝔰𝔩(2|1)-module vanishes. This vanishing happens for any value of q (even when q is not a root of unity). These properties make it difficult to create a fusion or modular category. Loosely speaking, the standard way to obtain such a category from a quantum group is: (1) specialize q to a root of unity; this forces some modules to have zero quantum dimension, (2) quotient by morphisms of modules with zero quantum dimension, (3) show the resulting category is finite and semi-simple. In this paper, we show an analogous construction works in the context of Uq𝔰𝔩(2|1) by replacing the vanishing quantum dimension with a modified quantum dimension. In particular, we specialize q to a root of unity, quotient by morphisms of modules with zero modified quantum dimension and show the resulting category is generically finite semi-simple. Moreover, we show the categories of this paper are relative G-spherical categories. As a consequence, we obtain invariants of 3-manifold with additional structures.
Symplectic id:
1135950
Submitted to ORA:
Submitted
Publication Type:
Journal Article