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In this talk we will state a result characterising the variety of Lie algebras amongst all varieties of non-associative algebras. More specifically, the variety of Lie algebras is the only variety that simultaneously satisfies the following two properties: every subalgebra of a free algebra is free, and, for every ideal I in every algebra, I^2 is also free. After analysing the statement, we will discuss the methods used in the proof, which go from Gröbner bases for operads to computational methods in commutative algebra. Joint work with Vladimir Dotsenko (Université de Strasbourg, France).
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