Experiments with New Music Tablatures based on Frobenius Algebra (Guitar, Timpani, Trombone)

Experiments with New Music Tablatures based on Frobenius Algebra (Guitar, Timpani, Trombone)

There has been a resurgence of interest in Frobenius algebras in recent years due to applications in coding theory. 

On this note we consider the connections between hyperplanes and ideals in Frobenius and symmetric algebras over commutative rings. 


This allows us to develop a succinct, coordinate-free proof of a result of T. Nakayama that determines when the quotient of a symmetric algebra over a field is again symmetric. As a corollary, we show the class of central symmetric algebras is identical to the class of central simple algebras.