Isomorphisms of Discriminant Algebras

2016/12/05 by Biesel, Owen, Gioia, Alberto
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1612.01582

Abstract

For each natural number n, we define a category whose objects are discriminant algebras in rank n, i.e. functorial means of attaching to each rank-n algebra a quadratic algebra with the same discriminant. We show that the discriminant algebras defined in [2], [6], and [10] are all isomorphic in this category, and prove furthermore that in ranks n ≤ 3 discriminant algebras are unique up to unique isomorphism.

Related

• The discriminant controls automorphism groups of noncommutative algebras
• On the Classification of Algebras
• On finitude of the number of isomorphism classes in the category NT
• Invariants for isomorphism classes in the category \bcalNT
• A Norm Functor for Quadratic Algebras