QUANTIZATION OF CONTINUUM KAC–MOODY ALGEBRAS

Andrea Appel, Francesco Sala

Research output: Contribution to journalArticlepeer-review

Abstract

Continuum Kac–Moody algebras have been recently introduced by the authors and O. Schiffmann in [ASS18]. 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 g 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, which allows to define on g a topological quasi–triangular Lie bialgebra structure. We then construct an explicit quantization of g, 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.
Original languageEnglish
Number of pages35
JournalPure and applied mathematics quarterly
Publication statusAccepted/In press - 8 Oct 2019

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