On the clifford algebra of a diagonal binary and cubic form

Abstract EN

In this work, we study the Clifford algebra C of a diagonal binary and cubic form f (X, Y) = aX3 + bY3 over a commutative ring A such that 6ab is invertible.

We show that C is an Azumaya algebra.

Also, under some hypotheses, we answer affirmatively the question of Haile [4] by showing that if A = K is a field of characteristic p ∉ {2, 3} and if f is isotropic or represents d3 for some d ∈K – {0}, then the Clifford algebra C is similar to its center Z in Brauer group Br (Z) : [C] = [Z] in Br (Z).