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Solvable Lie algebras, products by generators, and some of its applications

Abstract

In this work, we enlarge the definition of products by generators of Lie algebras to the class of solvable Lie algebras. We analyze the number of independent invariant functions for the coadjoint representation of these algebras by means of the Maurer-Cartan equations and give some applications to product structures on Lie algebras.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 4, pp. 85–94, 2005.

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Campoamor-Stursberg, R. Solvable Lie algebras, products by generators, and some of its applications. J Math Sci 144, 4423–4430 (2007). https://doi.org/10.1007/s10958-007-0280-5

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Keywords

  • Product Structure
  • Cohomology Class
  • Maximal Rank
  • Casimir Operator
  • Coadjoint Representation