The University of Sydney
School of Mathematics and Statistics  
Algebra Seminar  
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University of Sydney Algebra Seminar

Grant Cairns (Latrobe University)

Friday 8th April, 12.05-12.55pm, Carslaw 275

Classification of a special family of graded Lie algebras

We classify those finite dimensional Lie algebras which have a basis x_1, ..., x_n with the following properties:

1. [ x_i, x_j ]=c_{i,j} x_{i+j} for some constants c_{i,j},
2. c_{1,j} is nonzero, for all 1 < j < n.

It turns out that there are only 6 such algebras of dimension n < 7. In each of the dimensions 7,8,9,10,11, there are infinitely many algebras, while in dimension n > 11, there are precisely 4 or 5 algebras, according to whether n is even or odd respectively. This is joint work with Barry Jessup (University of Ottawa).