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- W4297975631 abstract "Given an algebraic Lie algebra $mathfrak{g}$ over $mathbb{C}$, we canonically associate to it a Lie algebra $mathfrak{g}_{infty}$ defined over $mathbb{C}_{infty}$-the reduction of $mathbb{C}$ mod infinitely large prime, and show that for a class of Lie algebras $mathfrak{g}_{infty}$ is an invariant of the derived category of $mathfrak{g}$-modules. We give two applications of this construction. First, we show that the bounded derived category of $mathfrak{g}$-modules determines algebra $mathfrak{g}$ for a class of Lie algebras. Second, given a semi-simple Lie algebra $mathfrak{g}$ over $mathbb{C}$, we construct a canonical homomorphism from the group of automorphisms of the enveloping algebra $mathfrak{U}mathfrak{g}$ to the group of Lie algebra automorphisms of $mathfrak{g}$, such that its kernel does not contain a nontrivial semi-simple automorphism. As a corollary we obtain that any finite subgroup of automorphisms of $mathfrak{U}mathfrak{g}$ isomorphic to a subgroup of Lie algebra automorphisms of $mathfrak{g}.$" @default.
- W4297975631 created "2022-10-01" @default.
- W4297975631 creator A5071143950 @default.
- W4297975631 date "2017-05-22" @default.
- W4297975631 modified "2023-09-30" @default.
- W4297975631 title "On automorphisms of enveloping algebras" @default.
- W4297975631 doi "https://doi.org/10.48550/arxiv.1705.08035" @default.
- W4297975631 hasPublicationYear "2017" @default.
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