Quantization of continuum Kac-Moody algebras (Q2214885)

Continuum Kac-Moody algebras constitute a new class of algebraic structures of recent development [\textit{A. Appel} et al., Mosc. Math. J. 22, No. 2, 177--224 (2022; Zbl 1502.17020)], that generalize the notion of Borcherds-Kac-Moody algebras, in the sense that they can be realized in terms of colimits of the latter type of algebras. In this paper, the authors prove that any continuum Kac-Moody algebra is canonically endowed with a non-degenerate invariant bilinear form. They further construct a Drin'feld-Jimbo quantum group associated to a continuum Kac-Moody algebra. It is proved that such groups arise themselves as a colimit of Drin'feld-Jimbo quantum groups. The construction is compared with other constructions of quantum groups, and found to be equivalent for certain special cases.