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This is the construction / computation page for my joint paper with Roland van der Veen, Everything Around $sl_{2+}^\epsilon$ is DoPeGDO. Hooray! (PDF here).

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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 Notebook (.pdf)Source (.nb)CreatedLast ModifiedSummary
1 Gam source 2021-05-13 08:45:47 2021-06-10 11:11:26 Verifying the generating function for $am_\epsilon$.
2 GDOCompositions source 2019-12-19 11:38:04 2021-05-14 04:38:39 Testing the associativity of compositions in GDO. Based on GenericDoPeGDO.nb in pensieve://Talks/DaNang-1905/.
3 index source 2019-12-16 20:24:42 2020-03-08 21:52:51 This is the index file for the DPG project.
4 nb2tex source 2020-02-11 09:57:26 2021-05-14 05:16:30 nb2tex for the DPG project.

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  1. Studied 2021-06-22 10:55:00: quantum field theory - Seeking a Precedent - Two-Stage Gaussian Integration- - MathOverflow.
  2. Studied 2021-06-22 11:25:26: Abdesselam, SLC49c.

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