Abstract:

Let E be a n-dimensional vector space over a field k and ω a trivector of Λ3E. We can associate to the trivector ω several invariants either algebraic, arithmetic or geometric. In this paper we consider the following three invariants, the commutant C(ω), the complexity c(ω) and the automorphisms group Aut(ω). We show that there exists a vector space E and a trivector ω of Λ3E for which C(ω) is not a Frobenius algebra. We also show that the complexity c(ω) and the length l(ω) are equal. Finally, we prove the existence of a trivector ω such that Aut(ω) is not a FC-group.