Lifting Lie algebras over the residue field of a discrete valuation ring

1999/01/21 by William Browder, Browder, William, Jonathan Pakianathan +1
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #K-Theory and Homology (math.KT) #Polynomial and algebraic computation #math.KT

paper · pdf · doi:10.48550/arxiv.math/9901145

arxiv created 1999/01/21 · openalex publication_date 1999/01/21 · arxiv updated 2016/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Studies among other things, the question of whether a Lie algebra over Z/(p^k)Z lifts to one over Z/(p^(k+1))Z. An obstruction theory is developed and examples of Fp-Lie algebras which don't lift to Lie algebras over Z/p²Z are discussed. An example of an application of the result: A Fp-Lie algebra L with H³(L, ad)=0 will lift to a p-adic Lie algebra.

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