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Quantum hyperdeterminants and hyper-Pfaffians

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Abstract

The notion of generalized quantum monoids is introduced. It is proved that the quantum coordinate ring of the monoid can be lifted to a quantum hyper-algebra, in which the quantum determinant and quantum Pfaffian are sent to the quantum hyperdeterminant and quantum hyper-Pfaffian respectively. The quantum hyperdeterminant in even dimension is shown to be a q-analog of Cayley’s first hyperdeterminant.

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Acknowledgements

This work is supported by NSFC Grant Nos. 11271138 and 11531004, and Simons Foundation 198129. The second author thanks the hospitality of North Carolina State University and support from China Scholarship Council during the project.

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Authors and Affiliations

  1. Department of Mathematics, North Carolina State University, Raleigh, NC, 27695, USA

    Naihuan Jing

  2. Department of Mathematics, Shanghai University, Shanghai, 200444, China

    Naihuan Jing

  3. Institute of Mathematics and Statistics, University of Sao Paulo, Sao Paulo, 05315-970, Brazil

    Jian Zhang

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  1. Naihuan Jing
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  2. Jian Zhang
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Correspondence to Jian Zhang.

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Jing, N., Zhang, J. Quantum hyperdeterminants and hyper-Pfaffians. Math. Z. 287, 897–914 (2017). https://doi.org/10.1007/s00209-017-1850-y

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  • DOI: https://doi.org/10.1007/s00209-017-1850-y

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