שלחו לחבר

Octonion algebras via G_2-torsors and triality

Seminar
Speaker
Dr. Seidon Alsaody (Institut Camille Jordan, Université Lyon 1)
Date
30/05/2018 - 11:00 - 10:00
Place
Room 132, Center for IT Infrastructure
Abstract

An octonion algebra is a unital, non-associative algebra endowed with a non-degenerate, multiplicative quadratic form. Such algebras are crucial in the construction of exceptional groups. Over fields, it is known that the quadratic form determines the algebra structure completely. Remarkably, this is not true over commutative rings in general, as was shown by P. Gille in 2014 using cohomological arguments.

I will talk about a recent joint work with Gille, where we give an explicit construction of all octonion algebras having the same quadratic form. I will explain the point of view of torsors and cohomology, and how the phenomenon of triality plays a key role in relating this to a classical construction of alternative algebras.

תאריך עדכון אחרון : 29/05/2018