Formalising Lie algebras
Abstract
Lie algebras are an important class of algebras which arise throughout mathematics and physics. We report on the formalisation of Lie algebras in Lean's Mathlib library. Although basic knowledge of Lie theory will benefit the reader, none is assumed; the intention is that the overall themes will be accessible even to readers unfamiliar with Lie theory. Particular attention is paid to the construction of the classical and exceptional Lie algebras. Thanks to these constructions, it is possible to state the classification theorem for finitedimensional semisimple Lie algebras over an algebraically closed field of characteristic zero. In addition to the focus on Lie theory, we also aim to highlight the unity of Mathlib. To this end, we include examples of achievements made possible only by leaning on several branches of the library simultaneously.
 Publication:

arXiv eprints
 Pub Date:
 December 2021
 DOI:
 10.48550/arXiv.2112.04570
 arXiv:
 arXiv:2112.04570
 Bibcode:
 2021arXiv211204570N
 Keywords:

 Computer Science  Logic in Computer Science;
 Mathematics  Representation Theory
 EPrint:
 12 pages, 1 figure, to appear in CPP 2022