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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).
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