Quantized universal enveloping algebras, the Yang-Baxter equation and invariants of links, I

Arun Ram
Department of Mathematics and Statistics
University of Melbourne
Parkville, VIC 3010 Australia
aram@unimelb.edu.au

Last update: 2 June 2014

Notes and References

This is a typed copy of the LOMI preprint Quantized universal enveloping algebras, the Yang-Baxter equation and invariants of links, I by N.Yu. Reshetikhin.

Recommended for publication by the Scientific Council of Steklov Mathematical Institute, Leningrad Department (LOMI) 6, June, 1987.

Contents

	Introduction
1.	Solutions of the Yang-Baxter equation connected with the $q\text{-deformation}$ of the universal enveloping algebras of simple Lie algebras
2.	Graphical representation of the $R\text{-matrices}$
3.	The $q\text{-analog}$ of Brauer-Weyl duality
4.	$𝔤=𝔤𝔩\left(n\right)$
5.	$𝔤=𝔰𝔬(2n+1)$ and $𝔤=𝔰𝔬\left(2n\right)$
6.	$𝔤=𝔰𝔭\left(2n\right)$
7.	$𝔤=G_2$
8.	Solutions of the Yang-Baxter equation, representations of the braid group and invariants of links.
9.	Invariants of links connected with $q\text{-deformations}$ of classical Lie algebras.
10.	An invariant of links corresponding to the algebra $G_2$
11.	Conclusion

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