A characterisation of Lie algebras via algebraic exponentiation

GarcΓ­a-MartΓ­nez, Xabier;Van der Linden, Tim
(2019) Advances in mathematics β€” Vol. 341, p. 92-117 (2019)

Files

43AcharacterisationofLiealgebrasviaalgebraicexponentiation.pdf
  • Closed Access
  • Adobe PDF
  • 487.16 KB
Request a copy
171100689.pdf
  • Open Access
  • Adobe PDF
  • 290.67 KB
Download

Details

Authors
Abstract
In this article we describe varieties of Lie algebras via algebraic exponentiation, a concept introduced by Gray in his Ph.D. thesis. For 𝕂 an infinite field of characteristic different from 2, we prove that the variety of Lie algebras over 𝕂 is the only variety of non-associative 𝕂-algebras which is a non-abelian locally algebraically cartesian closed (LACC) category. More generally, a variety of n-algebras V is a non-abelian (LACC) category if and only if n=2 and V=𝖫𝗂𝖾_𝕂. In characteristic 2 the situation is similar, but here we have to treat the identities xx=0 and xy=βˆ’yx separately, since each of them gives rise to a variety of non-associative 𝕂-algebras which is a non-abelian (LACC) category.
Affiliations

Citations

  • APA
  • Chicago
  • FWB

GarcΓ­a-MartΓ­nez, X., & Van der Linden, T. (2019). A characterisation of Lie algebras via algebraic exponentiation. Advances in mathematics, 341, 92-117. https://doi.org/10.1016/j.aim.2018.10.034 (Original work published 2019)