Generalized Knot Symmetric Algebras

Abstract

Attempts have been made to introduce a new class of algebras $$K_n$$, which we define as generalized knot symmetric algebras. The reason for this name is that these new algebras have a basis consisting of knot diagrams. The multiplication of two of these graphs turns $$K_n$$ into an associative. The semi-simplicity of these algebras over $$K_n$$ has been proved by making use of conditional exception and proving the non-degeneracy of the trace.