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math.QA2026★ 2 cited
Compact Quantum Homogeneous Kähler Spaces
Biswarup Das, Réamonn à Buachalla, Petr Somberg
Noncommutative Kähler structures were recently introduced as an algebraic framework for studying noncommutative complex geometry on quantum homogeneous spaces. In this paper, we i…
math.QA2025
Lusztig's Quantum Root Vectors and a Dolbeault Complex for the A-Series Full Quantum Flag Manifolds
Réamonn à Buachalla, Petr Somberg
For the Drinfeld-Jimbo quantum enveloping algebra , we show that the span of Lusztig's positive root vectors, with respect to Littlemann's nice reduced decomp…
math.QA2024
Braided coproduct, antipode and adjoint action for
Pavle PandžiÄ, Petr Somberg
Motivated by our attempts to construct an analogue of the Dirac operator in the setting of , we write down explicitly the braided coproduct, antipode, and adj…