2019 Thematic Program (I)

On free associative algebras

[TMCSC]

March 05, 2019  16:00-17:00

W303  School of Mathematics, Sichuan University

[lecture]20190305Olivier Mathieu-01.png

SPEAKER

Olivier Mathieu (University of Lyon I, France)

ABSTRACT

In this work, we define some abstract algebraic object. Conjecturally, we expect these object to describe free alternative and free Jordan algebras. The conjecture has been checked in some cases. For one generator free Jordan and alternative algebras, the conjecture holds: this approach provides a complex proof of the quite trivial fact that the free Jordan/alternative algebra in one variable is the one variable polynomial algebra. Also for free algebras with more than one generators, some numerical consequences has been checked by computer. For example, the conjecture is compatible with the existence Glennie identities (some degree 8 Jordan polynomial in three variables) and with the fact that tetrads are not Jordan polynomials.

ORGANIZERD BY

An-Min Li (Chair) (Sichuan University)

Bohui Chen (Sichuan University)

Xiaojun Chen (Sichuan University)

Farkhod Eshmatov (Sichuan University)

Wenchuan Hu (Sichuan University)

Raphael Ponge (Sichuan University)

SUPPORTED BY

Natural Science Foundation of China

School of Mathematics, Sichuan University

Tianyuan Mathematical Center in Southwest China