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Anomaly-free TQFTs from the super Lie algebra 𝔰𝔩(2|1)

. It is known that the category C H of nilpotent weight modules over the quantum group associated with the super Lie algebra sl (2 | 1) is a relative pre-modular G -category. Its modiﬁed trace enables to deﬁne an invariant of 3-manifolds. In this article we show that the category C H is a relative modular G -category which allows one to construct a family of non-semi-simple extended topological quantum ﬁeld theories which surprisingly are anomaly free. The quantum group associated with sl (2 | 1) is considered at odd roots of unity.