# Higher structures, quantum groups and genus zero modular operad

@article{Manin2019HigherSQ, title={Higher structures, quantum groups and genus zero modular operad}, author={Yuri I. Manin}, journal={Journal of the London Mathematical Society}, year={2019}, volume={100} }

In my Montreal lecture notes of 1988, it was suggested that the theory of linear quantum groups can be presented in the framework of the category of quadratic algebras (imagined as algebras of functions on ‘quantum linear spaces), and quadratic algebras of their inner (co)homomorphisms.

## 3 Citations

Genus zero modular operad and absolute Galois group

- Mathematics
- 2019

In this article, we develop the geometry of canonical stratifications of the spaces $\overline{\mathcal{M}}_{0,n}$ and prepare ground for studying the action of the Galois group…

Monoidal structures on the categories of quadratic data

- Mathematics
- 2019

The notion of 2--monoidal category used here was introduced by B. Vallette in 2007 for applications in the operadic context. The starting point for this article was a remark by Yu. Manin that in the…

Homotopy invariants for $\overline{\mathcal{M}}_{0,n}$ via Koszul duality.

- Mathematics
- 2019

We show that the integral cohomology rings of the moduli spaces of stable rational marked curves are Koszul. This answers an open question of Manin. Using the machinery of Koszul spaces developed by…

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Monoidal structures on the categories of quadratic data

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The notion of 2--monoidal category used here was introduced by B. Vallette in 2007 for applications in the operadic context. The starting point for this article was a remark by Yu. Manin that in the…