Second cohomology for finite groups of Lie type

  title={Second cohomology for finite groups of Lie type},
  author={Brian D. Boe and Brian Bonsignore and Theresa Brons and Jon F. Carlson and Leonard Chastkofsky and Christopher M. Drupieski and Niles Johnson and Daniel K. Nakano and Wenjing Li and Phong Thanh Luu and Tiago Macedo and Nham Vo Ngo and Brandon L. Samples and Andrew J. Talian and Lisa Townsley and Benjamin J. Wyser},
  journal={Journal of Algebra},
  • Brian D. Boe, Brian Bonsignore, +13 authors Benjamin J. Wyser
  • Published 2011
  • Mathematics
  • Journal of Algebra
  • Let $G$ be a simple, simply-connected algebraic group defined over $\mathbb{F}_p$. Given a power $q = p^r$ of $p$, let $G(\mathbb{F}_q) \subset G$ be the subgroup of $\mathbb{F}_q$-rational points. Let $L(\lambda)$ be the simple rational $G$-module of highest weight $\lambda$. In this paper we establish sufficient criteria for the restriction map in second cohomology $H^2(G,L(\lambda)) \rightarrow H^2(G(\mathbb{F}_q),L(\lambda))$ to be an isomorphism. In particular, the restriction map is an… CONTINUE READING