2-Generation of simple Lie algebras and free dense subgroups of algebraic groups

Alla Detinko; Willem de Graaf

doi:10.1016/j.jalgebra.2019.06.012

2-Generation of simple Lie algebras and free dense subgroups of algebraic groups

Alla Detinko, Willem de Graaf

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

We construct generating pairs of simple Lie algebras in characteristic zero. We apply this construction to exhibit infinite series of 2-generator Zariski dense subgroups that are free of rank 2 of the simple algebraic groups SL(n, C), Sp(n, C),
G2(C).

Original language	English
Pages (from-to)	159-173
Number of pages	15
Journal	Journal of Algebra
Volume	545
Early online date	21 Jun 2019
DOIs	https://doi.org/10.1016/j.jalgebra.2019.06.012
Publication status	Published - 1 Mar 2020
Externally published	Yes

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title = "2-Generation of simple Lie algebras and free dense subgroups of algebraic groups",

abstract = "We construct generating pairs of simple Lie algebras in characteristic zero. We apply this construction to exhibit infinite series of 2-generator Zariski dense subgroups that are free of rank 2 of the simple algebraic groups SL(n, C), Sp(n, C),G2(C).",

keywords = "Semisimple Lie algebras, Algebraic groups, Free dense subgroups",

author = "Alla Detinko and {de Graaf}, Willem",

year = "2020",

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day = "1",

doi = "10.1016/j.jalgebra.2019.06.012",

language = "English",

volume = "545",

pages = "159--173",

journal = "Journal of Algebra",

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T1 - 2-Generation of simple Lie algebras and free dense subgroups of algebraic groups

AU - Detinko, Alla

AU - de Graaf, Willem

PY - 2020/3/1

Y1 - 2020/3/1

N2 - We construct generating pairs of simple Lie algebras in characteristic zero. We apply this construction to exhibit infinite series of 2-generator Zariski dense subgroups that are free of rank 2 of the simple algebraic groups SL(n, C), Sp(n, C),G2(C).

AB - We construct generating pairs of simple Lie algebras in characteristic zero. We apply this construction to exhibit infinite series of 2-generator Zariski dense subgroups that are free of rank 2 of the simple algebraic groups SL(n, C), Sp(n, C),G2(C).

KW - Semisimple Lie algebras

KW - Algebraic groups

KW - Free dense subgroups

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U2 - 10.1016/j.jalgebra.2019.06.012

DO - 10.1016/j.jalgebra.2019.06.012

M3 - Article

SN - 0021-8693

VL - 545

SP - 159

EP - 173

JO - Journal of Algebra

JF - Journal of Algebra

ER -

2-Generation of simple Lie algebras and free dense subgroups of algebraic groups

Abstract

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