• 2-KNOT SYMMETRIC ALGEBRAS

*R. SELVARANI, M. KAMARAJ

Abstract


In this paper, we introduce a new class of algebras Kn, which we call 2-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 Kn into an associative algebra. By making use of conditional expectation and proving the non-degeneracy of the trace, we and also prove the semi simplicity of these algebras over Kn(x).


Keywords


Multiplication in Kn, Brauer algebra, knot graphs, semi simple.

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