Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 22 (2026), 092, 13 pages      arXiv:2601.07803      https://doi.org/10.3842/SIGMA.2026.092

Integration à la Harish-Chandra for Bi-Graded Lie Algebras

Alexei Kotov a, Vladimir Salnikov b and Olga Salnikova Chekeres bc
a) Faculty of Science, University of Hradec Králové, Rokitanskeho 62, Hradec Králové, 50003, Czech Republic
b) LaSIE UMR 7356 CNRS / La Rochelle University, Avenue Michel Crépeau, La Rochelle, 17042, France
c) M&MoCS Center, Università degli Studi dell'Aquila, Piazzale Ernesto Pontieri, Monteluco di Roio, L'Aquila, 67100, Italy

Received January 27, 2026, in final form September 09, 2026; Published online September 24, 2026

Abstract
We study $\mathbb{Z}_2\times\mathbb{Z}_2$ bi-graded Lie algebras. We describe their properties in relation to Lie superalgebras with some compatible structures. Then we focus on the approach to the Lie group-algebra correspondence based on Harish-Chandra pairs and provide some examples of application of it in the bi-graded setting.

Key words: multi-graded manifolds; Harish-Chandra pairs.

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