The groupL(2 61) embeds in t h e Lie group of typeE8

DOI10.1080/00927879308824659zbMath0805.20015OpenAlexW2167353525MaRDI QIDQ5286455

Arjeh M. Cohen, Robert L. jun. Griess, Bert Lisser

Publication date: 29 June 1993

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00927879308824659

zbMATH Keywords

presentationfinite fieldsLie algebraMathematicaMapleChevalley groupCoxeter numberlinear fractional transformationsGAPBorel subgroupChevalley basissimple complex Lie groupLiEfinite simple group \(L(2,61)\)Lie group of type \(E_ 8\)unique conjugacy class of subgroups

Mathematics Subject Classification ID

Linear algebraic groups over finite fields (20G40) Subgroup theorems; subgroup growth (20E07) Simple groups (20E32) Discrete subgroups of Lie groups (22E40) Lie algebras of Lie groups (22E60) General properties and structure of complex Lie groups (22E10) Finite simple groups and their classification (20D05) Simple groups: alternating groups and groups of Lie type (20D06) Simple, semisimple, reductive (super)algebras (17B20)

Related Items (9)

On some exotic finite subgroups of \(E_8\) and Springer's regular elements of the Weyl group. ⋮ Kostant's conjecture and L₂(q) invariant theory in the rank two lie groups ⋮ Embeddings of \(\text{PGL}_2(31)\) and \(\text{SL}_2(32)\) in \(E_8(\mathbb{C})\). With appendices by Michael Larsen and J. -P. Serre ⋮ Embeddings of the group \(L(2,13)\) in groups of Lie type \(E_ 6\) ⋮ Embeddings of \(\text{PSL}(2,41)\) and \(\text{PSL}(2,49)\) in \(E_8(\mathbb{C})\) ⋮ Can one see the signs of structure constants? ⋮ Conjugacy of \(\text{Alt}_5\) and \(\text{SL}(2,5)\) subgroups of \(E_6(\mathbb{C})\), \(F_4(\mathbb{C})\), and a subgroup of \(\mathbb{E}_8(\mathbb{C})\) of type \(A_2E_6\) ⋮ Chevalley groups over commutative rings. I: Elementary calculations ⋮ Finite simple groups which projectively embed in an exceptional Lie group are classified!

Uses Software

• GAP
• Maple
• Mathematica
• LiE

Cites Work

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• Elementary abelian p-subgroups of algebraic groups
• Unitary representations of some infinite dimensional groups
• Regular elements of finite reflection groups
• Reductive groups over a local field
• The Principal Three-Dimensional Subgroup and the Betti Numbers of a Complex Simple Lie Group
• Finite subgroups of G₂,(c)

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