Shiyuan Liu

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math.RT2026

Quasi-Whittaker supermodules over Lie superalgebras

Wenting Gao, Baiying He, Shiyuan Liu +1

In this paper, we develop a general theory of quasi-Whittaker supermodules over Lie superalgebras induced from an arbitrary ideal. We determine the quasi-Whittaker vectors in unive…

math.RT2025

Quasi-Whittaker modules

Cunguang Cheng, Wenting Gao, Shiyuan Liu +2

In this paper, a general setting is proposed to define a class of modules over nonsemisimple Lie algebras $g$ induced by a nonperfect ideal $p$ . This class of…

math.RT2025

Simple smooth modules over the Lie algebras of polynomial vector fields

Zhiqiang Li, Cunguang Cheng, Shiyuan Liu +3

Let $g := Der (C [t_{1}, t_{2}, \dots, t_{n}])$ and $L := Der (C [[t_{1}, t_{2}, \dots, t_{n}]])$ be the Witt Lie algebras. Clearly, $g$ i…

math.RT2024

Symmetric Biderivations on Complex Semisimple Lie Algebras

Liu Shiyuan, Liu Dong, Zhao Yueqiang

This paper studies biderivations on finite-dimensional complex semisimple Lie algebras to their finite-dimensional modules. More precisely, we prove that all such symmetric bideriv…