The wonderful compactification for quantum groups

I.V. Ganev, Journal of the London Mathematical Society 99 (2019) 778–806.

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Abstract
In this paper, we introduce a quantum version of the wonderful compactification of a group as a certain noncommutative projective scheme. Our approach stems from the fact that the wonderful compactification encodes the asymptotics of matrix coefficients, and from its realization as a GIT quotient of the Vinberg semigroup. In order to define the wonderful compactification for a quantum group, we adopt a generalized formalism of Proj categories in the spirit of Artin and Zhang. Key to our construction is a quantum version of the Vinberg semigroup, which we define as a q-deformation of a certain Rees algebra, compatible with a standard Poisson structure. Furthermore, we discuss quantum analogues of the stratification of the wonderful compactification by orbits for a certain group action, and provide explicit computations in the case of SL2.
Publishing Year
Date Published
2019-06-01
Journal Title
Journal of the London Mathematical Society
Volume
99
Issue
3
Page
778-806
IST-REx-ID
5

Cite this

Ganev IV. The wonderful compactification for quantum groups. Journal of the London Mathematical Society. 2019;99(3):778-806. doi:10.1112/jlms.12193
Ganev, I. V. (2019). The wonderful compactification for quantum groups. Journal of the London Mathematical Society, 99(3), 778–806. https://doi.org/10.1112/jlms.12193
Ganev, Iordan V. “The Wonderful Compactification for Quantum Groups.” Journal of the London Mathematical Society 99, no. 3 (2019): 778–806. https://doi.org/10.1112/jlms.12193.
I. V. Ganev, “The wonderful compactification for quantum groups,” Journal of the London Mathematical Society, vol. 99, no. 3, pp. 778–806, 2019.
Ganev IV. 2019. The wonderful compactification for quantum groups. Journal of the London Mathematical Society. 99(3), 778–806.
Ganev, Iordan V. “The Wonderful Compactification for Quantum Groups.” Journal of the London Mathematical Society, vol. 99, no. 3, Wiley, 2019, pp. 778–806, doi:10.1112/jlms.12193.
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