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 inNational Academy of Sciences, India. Proceedings. Section A. Physical Sciences Vol. 90; no. 1; pp. 149 - 156
Main Authors Selvarani, R., Kamaraj, M.
Format Journal Article Conference Proceeding
LanguageEnglish
Published New Delhi Springer India 01.03.2020
Springer Nature B.V
Subjects
Algebra
Applied and Technical Physics
Atomic
Knots
Molecular
Multiplication
Optical and Plasma Physics
Physics
Physics and Astronomy
Quantum Physics
Research Article
Trace and semi-simple
Types of knots
Generalized knot diagram
Generalized knot mapping
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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