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Temperley-Lieb Algebras.pdf

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Preview of Temperley-Lieb Algebras
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Summary

The Temperley-Lieb Algebra of Type A, TLn(A), is an associative algebra generated by elements e1, e2, ..., en-1 with relations e2i = δei, eiej = ejei for |i - j| ≥ 2, and eiejei = ei for |i - j| = 1. TLn(A) is a finite dimensional algebra over Z[δ] with rank equal to the nth Catalan number. It was introduced by Temperley and Lieb in 1971 and has applications in physics, knot theory, and other areas. A diagram algebra model of TLn(A) was developed by Penrose and Kauffman, and it is isomorphic to a quotient of the Hecke Algebra of type An-1.

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The Temperley-Lieb Algebra of Type A, TLn(A), is an associative algebra generated by elements e1, e2, ..., en-1 with relations e2i = δei, eiej = ejei for |i -...

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