Non-commutative amoebas

Grigory Mikhalkin; Mikhail Shkolnikov

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arXiv · 2102.09324

Non-commutative amoebas

Grigory Mikhalkin·Mikhail Shkolnikov

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Abstract

The group of isometries of the hyperbolic 3-space is one of the simplest non-commutative complex Lie groups. Its quotient by the maximal compact subgroup naturally maps it back to the hyperbolic space. Each fiber of this map is diffeomorphic to the real projective 3-space. The resulting map can be viewed as the simplest non-commutative counterpart of the amoeba map introduced, in the commutative setting, by Gelfand, Kapranov and Zelevinsky. The paper surveys basic properties of the non-commutative amoebas and compares them against their commutative counterparts.

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BibTeX RIS

Grigory Mikhalkin, Mikhail Shkolnikov. 2021-02-18. Non-commutative amoebas. https://arxiv.org/abs/2102.09324

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