Nie jesteś zalogowany | zaloguj się

Wydział Matematyki, Informatyki i Mechaniki Uniwersytetu Warszawskiego

  • Skala szarości
  • Wysoki kontrast
  • Negatyw
  • Podkreślenie linków
  • Reset

Aktualności — Wydarzenia

Sem. Algebra

 

Pre-Lie rings and classification of braces


Prelegent: Dora Puljic

2023-06-01 12:15

Braces are algebraic objects introduced by W. Rump in 2007 to help the study of non-degenerate, involutive, set theoretic solutions to the Yang-Baxter equation. Braces have been linked to many other objects of interest - Hopf-Galois extensions, braid groups, quantum groups, trusses, etc. In this talk we focus on the connection between braces and pre-Lie rings. It has been shown that nilpotent pre-Lie rings of cardinality p^n correspond to strongly nilpotent braces of the same cardinality, for sufficiently large primes p. These braces are explicitly obtained from the corresponding pre-Lie rings by the construction of the group of flows. In this talk we introduce braces and pre-Lie rings, and describe the passage between them. As an application we describe how this connection is leveraged for the classification of braces of cardinality p^4.