Twisted Hochschild Homology of Quantum Flag Manifolds and Kähler Forms

Symmetry Integrability and Geometry-Methods and Applications

article

Marco Matassa¹ 

[1] OsloMet - Oslo Metropolitan University

关键词: quantum flag manifolds;    twisted Hochschild homology;    K¨ahler forms 2020 Mathematics Subject Classification 17B37;    20G42;    16E40;   

DOI  :  10.3842/SIGMA.2020.098

来源: National Academy of Science of Ukraine

【 摘 要 】

We study the twisted Hochschild homology of quantum flag manifolds, the twist being the modular automorphism of the Haar state. We prove that every quantum flag manifold admits a non-trivial class in degree two, with an explicit representative defined in terms of a certain projection. The corresponding classical two-form, via the Hochschild-Kostant-Rosenberg theorem, is identified with a Kähler form on the flag manifold.

【 授权许可】

Unknown