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Determinants, integrality and Noether’s theorem for quantum commutative algebras

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Abstract

The aim of this paper is to generalize Noether’s theorem for finite groups acting on commutative algebras, to finite-dimensional triangular Hopf algebras acting on quantum commutative algebras. In the process we construct a non-commutative determinant function which yields an analogue of the Cayley-Hamilton theorem for certain endomorphisms.

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Author information

Author notes

  1. Shenglin Zhu

    Present address: Department of Mathematics, Fudan University, Shanghai, PR China

Authors and Affiliations

  1. Department of Mathematics and Computer Science, Ben Gurion University of the Negev, 84105, Beer Sheva, Israel

    Miriam Cohen & Shenglin Zhu

  2. Interdisciplinary Department of the Social Science, Bar-Ilan University, 52900, Ramat-Gan, Israel

    Sara Westreich

Authors
  1. Miriam Cohen
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  2. Sara Westreich
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  3. Shenglin Zhu
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Corresponding author

Correspondence to Miriam Cohen.

Additional information

In memory of Professor Shimshon Amitsur

The author was supported by the Plan and Budget Committee of the Israeli Government.

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Cohen, M., Westreich, S. & Zhu, S. Determinants, integrality and Noether’s theorem for quantum commutative algebras. Israel J. Math. 96, 185–222 (1996). https://doi.org/10.1007/BF02785538

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  • DOI: https://doi.org/10.1007/BF02785538

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