Abstract
It is known that the category [Formula: see text] of nilpotent weight modules over the quantum group associated with the super Lie algebra [Formula: see text] is a relative pre-modular [Formula: see text]-category. Its modified trace enables one to define an invariant of [Formula: see text]-manifolds. In this paper, we show that the category [Formula: see text] is a relative modular [Formula: see text]-category which allows one to constructing a family of non-semi-simple extended topological quantum field theories, and the family of TQFTs is anomaly free. The quantum group associated with [Formula: see text] is considered at odd roots of unity.
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