Abstract
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.
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Acknowledgements
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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Communicated by Christoph Schweigert.
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Ha, N.P. Topological invariants from quantum group \(\mathcal {U}_{\xi }\mathfrak {sl}(2|1)\) at roots of unity. Abh. Math. Semin. Univ. Hambg. 88, 163–188 (2018). https://doi.org/10.1007/s12188-017-0181-6
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DOI: https://doi.org/10.1007/s12188-017-0181-6