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Abstract. We construct $sl_{2+}^\epsilon$, a certain "lossless approximation" of $sl_2$, and show that "everything that matters" around its universal enveloping algebra and its quantization, namely the products, the co-products, the $R$-matrix, and other essential ingredients, can be described in terms of a certain category DoPeGDO of "Docile Perturbed Gaussian differential operators".
Those essential ingredients are what one needs in order to construct powerful knot invariants with good algebraic properties. Also, as we show, DoPeGDO is "easy" in the sense of computational complexity. Hence we get (and implement and compute) powerful poly-time-computatble knot invariants with favourable algebraic properties. Hooray!
Similar constructions ought to exist for all semi-simple Lie algebras, but we do not pursue this here.
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Archive DiamondBranch figs nb2tex_pdfs / Talks: DaNang-1905 Projects: nb2tex Projects: SL2PO DPG.pdf DPGTagged.pdf / recycling.txt<< Mathematica Notebooks >>
| Notebook (.pdf) | Source (.nb) | Created | Last Modified | Summary | |
|---|---|---|---|---|---|
| 1 | Gam | source | Sun 17 Mar 2024 11:28:50 | Thu 10 Jun 2021 11:11:26 | Verifying the generating function for $am_\epsilon$. |
| 2 | GDOCompositions | source | Sun 17 Mar 2024 11:28:50 | Fri 14 May 2021 04:38:39 | Testing the associativity of compositions in GDO. Based on GenericDoPeGDO.nb in pensieve://Talks/DaNang-1905/. |
| 3 | index | source | Sun 17 Mar 2024 11:28:50 | Sun 8 Mar 2020 21:52:51 | This is the index file for the DPG project. |
| 4 | nb2tex | source | Sun 17 Mar 2024 11:28:50 | Fri 14 May 2021 05:16:30 | nb2tex for the DPG project. |
<< Links >>
- Studied Tue 22 Jun 2021 10:55:00: quantum field theory - Seeking a Precedent - Two-Stage Gaussian Integration- - MathOverflow.
- Studied Tue 22 Jun 2021 11:25:26: Abdesselam, SLC49c.
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