1
$\begingroup$

It has been cited in several places (eg. https://arxiv.org/pdf/1912.05519.pdf) that the S-module Ass is isomorphic to the composite of the S-modules Com and Lie. Is there a reference which gives the actual isomorphism? Please help.

Improve this question
$\endgroup$
1
  • 1
    $\begingroup$ This is essentially the Poincaré-Birkhoff-Witt theorem: the tensor algebra on a finite set has a natural filtration such that the associated graded ring is the symmetric algebra generated by the free Lie algebra, and the filtration can be split if you do not care about preserving the ring structure. So you should look for information about the PBW theorem if you want formulae. $\endgroup$
    – Neil Strickland
    Commented May 17, 2022 at 17:55

0

Reset to default

You must log in to answer this question.

Browse other questions tagged .