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arXiv · 1903.01413

Quantization of continuum Kac-Moody algebras

Andrea Appel·Francesco Sala
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Abstract

Continuum Kac-Moody algebras have been recently introduced by the authors and O. Schiffmann. These are Lie algebras governed by a continuum root system, which can be realized as uncountable colimits of Borcherds-Kac-Moody algebras. In this paper, we prove that any continuum Kac-Moody algebra is canonically endowed with a non-degenerate invariant bilinear form. The positive and negative Borel subalgebras form a Manin triple with respect to this pairing, inducing on the continuum Kac-Moody algebra a topological quasi-triangular Lie bialgebra structure. We then construct an explicit quantization, which we refer to as a continuum quantum group, and we show that the latter is similarly realized as an uncountable colimit of Drinfeld-Jimbo quantum groups.

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BibTeXRIS

Andrea Appel, Francesco Sala. 2019-03-04. Quantization of continuum Kac-Moody algebras. https://doi.org/10.4310/pamq.2020.v16.n3.a5

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