Bulletin of the Korean Mathematical Society (대한수학회보)

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ANNIHILATOR IDEALS OF SIMPLE MODULES OF RESTRICTED QUANTIZED ENVELOPING ALGEBRA

  • Yu Wang (School of Mathematics and Physics Jiangsu University of Technology)
  • Received : 2022.07.03
  • Accepted : 2023.03.30
  • Published : 2023.07.31
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Abstract

Let U be the restricted quantized enveloping algebra Ũq(𝖘𝖑2) over an algebraically closed field of characteristic zero, where q is a primitive 𝑙-th root of unity (with 𝑙 being odd and greater than 1). In this paper we show that any indecomposable submodule of U under the adjoint action is generated by finitely many special elements. Using this result we describe all ideals of U. Moreover, we classify annihilator ideals of simple modules of U by generators.

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Acknowledgement

The author would like to express gratitude to Professor Libin Li for his helpful suggestions and constructive comments. The author also wishes to thank the reviewer for his or her careful review.

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