有限李型单群上的有限维pointed Hopf代数 VII. PSL(n,q)和PSp(2n,q)中的半单类
Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type VII. Semisimple classes in PSL(n,q) and PSp(2n,q)
AI总结：
该文研究有限李型单群上的有限维pointed Hopf代数分类，通过分析半单轨道上Nichols代数的维数性质，证明几类PSL、PSp群对应的有限维pointed Hopf代数均同构于群代数，完善了此前的分类工作。
摘要：
我们证明：有限域上射影特殊线性群上的单Yetter-Drinfeld模，若其支集为半单轨道且轨道中元素可约，则其Nichols代数为无限维；对于有限辛群中除低秩情形外的所有半单轨道，我们也得到了类似结果。我们证明射影特殊线性群中不可约元素的轨道无法用我们的方法处理。我们得出结论：所有群样元群同构于PSL(n,q)（n≥4）、PSL(3,q)（q>2）或PSp(2n,q)（n≥3）的有限维pointed Hopf代数H，都同构于群代数，完善了arXiv:1506.06794中的工作。
英文摘要：
We show that the Nichols algebra of a simple Yetter-Drinfeld module over a projective special linear group over a finite field whose support is a semisimple orbit has infinite dimension, provided that the elements of the orbit are reducible; we obtain a similar result for all semisimple orbits in a finite symplectic group except in low rank. We prove that orbits of irreducible elements in the projective special linear groups could not be treated with our methods. We conclude that any finite-dimensional pointed Hopf algebra H with group of grouplike elements isomorphic to PSL(n,q) (n greater than or equal to 4), PSL(3,q) (q greater than 2), or PSp(2n,q) (n greater than or equal to 3), is isomorphic to a group algebra, completing work in arXiv:1506.06794.
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