1998/09/16 by Caenepeel, S., Ion, B., Militaru, G.
#FOS: Mathematics #Quantum Algebra (math.QA) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.math/9809084
We present a unified apoach to the study of separable and Frobenius algebras. The crucial observation is thsat both cases are related to the nonlinear equation R12R23=R23R13=R13R12, called the FS-equation. Given a solution of the FS-equation satisfying certain normalizing conditions, we can construct a Frobenius algebra or a separable algebra A(R). The main result of this paper in the structure of this two fundamental types of algebras: a finitely generated projective Frobenius or separable k-algebra A is isomorphic to such A(R). If A is free as a k-module, then A(R) can be described using generators and relations. A new characterisation of Frobenius extensions is given: B⊂ A is Frobenius if and only if A has a B-coring structure such that the comultiplication Δ is an A-bimodule map.