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 language | English |
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Pages (from-to) | 633-639 |
Journal | American Mathematical Monthly |
Volume | 114 |
Issue number | 7 |
Publication status | Published - 2007 |