Generalized Knot Symmetric Algebras

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-s...

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Bibliographic Details
Published in:National Academy of Sciences, India. Proceedings. Section A. Physical Sciences India. Proceedings. Section A. Physical Sciences, 2020-03, Vol.90 (1), p.149-156
Main Authors: Selvarani, R., Kamaraj, M.
Format: Article
Language:English
Subjects:
Algebra
Applied and Technical Physics
Atomic
Knots
Molecular
Multiplication
Optical and Plasma Physics
Physics
Physics and Astronomy
Quantum Physics
Research Article
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Summary: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.
ISSN:0369-8203
2250-1762
DOI:10.1007/s40010-018-0552-0