## The Bianchi variety.(English)Zbl 1201.53084

Summary: The totality Lie($$V$$) of all Lie algebra structures on a vector space $$V$$ over a field $$\mathbb F$$ is an algebraic variety over $$\mathbb F$$ on which the group GL($$V$$) acts naturally. We give an explicit description of Lie($$V$$) for $$\dim V = 3$$ which is based on the notion of compatibility of Lie algebra structures.

### MSC:

 53D17 Poisson manifolds; Poisson groupoids and algebroids 17B99 Lie algebras and Lie superalgebras
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### References:

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