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Reseña: Formalising Lie algebras in Lean

Se ha publicado un artículo de razonamiento formalizado en Lean sobre álgebras de Lie titulado Formalising Lie algebras.

Su autor es Oliver Nash (Imperial College in London, U.K.).

Su resumen es

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 finite-dimensional 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.

El código de las correspondientes teorías se encuentra aquí.

El trabajo se presentará en el Certified Programs and Proofs (CPP) 2022 el 18 de enero de 2022.