Particle-like structure of Lie algebras

  title={Particle-like structure of Lie algebras},
  author={Alexandre M. Vinogradov},
  journal={Journal of Mathematical Physics},
  • A. Vinogradov
  • Published 13 July 2017
  • Mathematics
  • Journal of Mathematical Physics
If a Lie algebra structure 𝔤 on a vector space is the sum of a family of mutually compatible Lie algebra structures 𝔤i’s, we say that 𝔤 is simply assembled from the 𝔤i’s. Repeating this procedure with a number of Lie algebras, themselves simply assembled from the 𝔤i’s, one obtains a Lie algebra assembled in two steps from 𝔤i’s, and so on. We describe the process of modular disassembling of a Lie algebra into a unimodular and a non-unimodular part. We then study two inverse questions… 

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