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

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. $𝔤=𝔰𝔬\left(2n+1\right)$ 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