The Amitsur-Levitzki theorem, its proofs and applications
Vesselin Drensky (Bulgarian Academy of Sciences)
06/Sep/2024 - 10:00 GMT-3 (São Paulo time)

Slides: here.

The Amitsur-Levitzki theorem from 1950 states that the \(n\times n\) matrices over any field satisfy the standard identity of degree \(2n\) \[s_{2n}=\sum_{\sigma\in S_{2n}}(-1)^{\sigma}x_{\sigma(1)}\cdots x_{\sigma(2n)}=0,\] where \(S_{2n}\) is the symmetric group of degree \(2n\) and up to a multiplicative constant this is the only polynomial identity of minimal degree for the matrix algebra.

The purpose of the talk is to give several proofs of the Amitsur-Levitzki theorem due to Swan (1963), Razmyslov (1974), Rosset (1976), Szigeti, Tuza and Révész (1993) and to present some consequences of the theorem.



https://www.ime.usp.br/~fyyasumura/PISeminars