Shenglin Zhu

activity

20002026

collaborators

9 papers

math.RT2026

Affine Dual Braid Monoids: Finite Cores, Exceptional Cluster Complexes, and Koszul Resolutions

Jindong Yan, Shenglin Zhu

For every finite-rank crystallographic affine Coxeter system $(W, S)$ and Coxeter element $c$ , we construct a minimal linear graded free resolution of the trivial module over $k[M([…

math.RA2026

Standard Polynomials for Principal Subalgebras $K Q_{\geq 1}$ of Path Algebras

Yihao Zheng, Shenglin Zhu

We investigate standard polynomials for principal subalgebras of path algebras. First, we use standard polynomials to study the $P I$ -theory of principal subalgebras. Then we descri…

math.DG2026

Nilpotent Lie algebras obtained by ordered sets and Ricci solitons

Yihao Zheng, Shenglin Zhu

Nilpotent Lie groups with left-invariant metrics provide nontrivial examples of Ricci solitons. Some typical examples are given by the class of two-step nilpotent Lie algebras obta…

math.QA2022

Weak Hopf Algebras, Smash Products and Applications to Adjoint-Stable Algebras

Zhimin Liu, Shenglin Zhu

For a semisimple quasi-triangular Hopf algebra $(H, R)$ over a field $k$ of characteristic zero, and a strongly separable quantum commutative $H$ -module algebra $A$ ove…

math.QA2021

Centers of Braided Tensor Categories

Zhimin Liu, Shenglin Zhu

Let $C$ be a finite braided multitensor category. Let $B$ be Majid's automorphism braided group of $C$ , then $B$ is a cocommutative Hopf algebra in $\mathcal{C}…

math.RA2019

The applications of probability groups on Hopf algebras

Jingheng Zhou, Shenglin Zhu

In this work, we use probability groups, introduced by Harrison in 1979, as a tool to study a semisimple Hopf algebra $H$ with a commutative character ring and prove that the algeb…