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- W3045822607 abstract "A double extension ( $${mathscr {D}}$$ -extension) of a Lie (super)algebra $${mathfrak {a}}$$ with a non-degenerate invariant symmetric bilinear form $${mathscr {B}}$$ , briefly, a NIS-(super)algebra, is an enlargement of $${mathfrak {a}}$$ by means of a central extension and a derivation; the affine Kac–Moody algebras are the best known examples of double extensions of loops algebras. Let $${mathfrak {a}}$$ be a restricted Lie (super)algebra with a NIS $${mathscr {B}}$$ . Suppose $${mathfrak {a}}$$ has a restricted derivation $${mathscr {D}}$$ such that $${mathscr {B}}$$ is $${mathscr {D}}$$ -invariant. We show that the double extension of $${mathfrak {a}}$$ constructed by means of $${mathscr {B}}$$ and $${mathscr {D}}$$ is restricted. We show that, the other way round, any restricted NIS-(super)algebra with non-trivial center can be obtained as a $${mathscr {D}}$$ -extension of another restricted NIS-(super)algebra subject to an extra condition on the central element. We give new examples of $${mathscr {D}}$$ -extensions of restricted Lie (super)algebras, and pre-Lie superalgebras indigenous to characteristic 3." @default.
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- W3045822607 date "2020-06-01" @default.
- W3045822607 modified "2023-10-18" @default.
- W3045822607 title "Double Extensions of Restricted Lie (Super)Algebras" @default.
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- W3045822607 doi "https://doi.org/10.1007/s40598-020-00149-5" @default.
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