Abstract
For any finitely generated unital commutative associative algebra \(\mathcal {R}\) over \(\mathbb {C}\) and any complex finite-dimensional simple Lie algebra \(\mathfrak {g}\) with a fixed Cartan subalgebra \(\mathfrak {h}\), we classify all \(\mathfrak {g}\otimes \mathcal {R}\)-modules on \(U(\mathfrak {h})\) such that \(\mathfrak {h}\) as a subalgebra of \(\mathfrak {g}\otimes \mathcal {R}\), acts on \(U(\mathfrak {h})\) by the multiplication. We construct these modules explicitly and study their module structures.
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Acknowledgements
This paper was partially supported by the NSF of China (11931009, 12161141001, 12171132 and 11771410) and Innovation Program for Quantum Science and Technology (2021ZD0302902). The authors are also grateful to the referees for their valuable suggestions to improve the paper.
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Chen, H., Dai, H. & Liu, X. A Class of Polynomial Modules over Map Lie Algebras. Commun. Math. Stat. (2024). https://doi.org/10.1007/s40304-023-00356-4
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DOI: https://doi.org/10.1007/s40304-023-00356-4