Maximal tori determining the algebraic group

Details Maximal tori determining the algebraic group Maximal tori determining the algebraic group

2004-09-23

arxiv.org/abs/math/0409450v2

Pacific J. Math., 220:1, 69--85 (2005)

Mathematics

Group Theory

13 pages

Scientific paper

Let k be a finite field, a global field or a local non-archimedean field. Let H_1 and H_2 be two split, connected, semisimple algebraic groups defined over k. We prove that if H_1 and H_2 share the same set of maximal k-tori up to k-isomorphism, then the Weyl groups W(H_1) and W(H_2) are isomorphic, and hence the algebraic groups modulo their centers are isomorphic except for a switch of a certain number of factors of type B_n and C_n. We remark that due to a recent result of Philippe Gille, above result holds for fields which admit arbitrary cyclic extensions.

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