On a certain Lie algebra defined by a finite group

A.M. Cohen, D.E. Taylor

Research output: Contribution to journalArticleAcademicpeer-review

3 Citations (Scopus)
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Abstract

Some years ago W. Plesken told the first author of a simple but interesting construction of a Lie algebra from a finite group. The authors posed themselves the question as to what the structure of this Lie algebra might be. In particular, for which groups does the construction produce a simple Lie algebra? The answer is given in the present paper; it uses some textbook results on representations of finite groups, which we explain along the way. Little knowledge of the theory of Lie algebras is required beyond the dfinition of a Lie algebra itself and the definitions of simple and semisimple Lie algebras. Thus this exposition may serve as the basis for some entertaining examples er exercises in a graduate course on the representation theory of finite groups.
Original languageEnglish
Pages (from-to)633-639
JournalAmerican Mathematical Monthly
Volume114
Issue number7
Publication statusPublished - 2007

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