© | << < ? > >> | Dror Bar-Natan: Talks:

**Abstract.** Recently, Roland van der Veen and myself found that
there are sequences of solvable Lie algebras "converging" to any
given semi-simple Lie algebra (such as $sl_2$ or $sl_3$ or $E8$). Certain
computations are much easier in solvable Lie algebras; in particular,
using solvable approximations we can compute in polynomial time
certain projections (originally discussed by Rozansky) of the knot
invariants arising from the Chern-Simons-Witten topological quantum field
theory. This provides us with the first strong knot invariants that are
computable for truly large knots.

But $sl_2$ and $sl_3$ and similar algebras occur in physics (and in mathematics) in many other places, beyond the Chern-Simons-Witten theory. Do solvable approximations have further applications?

**Handout:**
SolvApp.html,
SolvApp.pdf,
SolvApp.png.

**Sources:** pensieve.