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Knit products of graded Lie algebras and groups

Michor, Peter W. (1990)

Proceedings of the Winter School "Geometry and Physics"

Let A = k A k and B = k B k be graded Lie algebras whose grading is in 𝒵 or 𝒵 2 , but only one of them. Suppose that ( α , β ) is a derivatively knitted pair of representations for ( A , B ) , i.e. α and β satisfy equations which look “derivatively knitted"; then A B : = k , l ( A k B l ) , endowed with a suitable bracket, which mimics semidirect products on both sides, becomes a graded Lie algebra A ( α , β ) B . This graded Lie algebra is called the knit product of A and B . The author investigates the general situation for any graded Lie subalgebras A and B of a graded...

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