Topological invariants from quantum group \(\mathcal {U}_{\xi }\mathfrak {sl}(2|1)\) at roots of unity

  • Ngoc Phu Ha


In this article we construct link invariants and 3-manifold invariants from the quantum group associated with the Lie superalgebra \(\mathfrak {sl}(2|1)\). The construction is based on nilpotent irreducible finite dimensional representations of quantum group \(\mathcal {U}_{\xi }\mathfrak {sl}(2|1)\) where \(\xi \) is a root of unity of odd order. These constructions use the notion of modified trace and relative \( G \)-modular category of previous authors.


Lie superalgebra Quantum group Link invariant 3-manifold 

Mathematics Subject Classification

57M27 17B37 



I would like to thank B. Patureau-Mirand, my thesis advisor, who helped me with this work, and who gave me the motivation to study mathematics. I would like to thank the referee for his constructive remarks. I would also like to thank my professors and friends in the laboratory LMBA of the Université de Bretagne Sud.


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Copyright information

© The Author(s) 2017

Authors and Affiliations

  1. 1.Laboratoire de Mathématiques de Bretagne AtlantiqueUniversité de Bretagne Sud, Centre de Recherche, Campus de TohannicVannesFrance

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