Open AccessOn the Dolbeault–Dirac operator of quantized symmetric spaces
Author(s) -
Krähmer Ulrich,
TuckerSimmons Matthew
Publication year - 2015
Publication title -
transactions of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.43
H-Index - 7
ISSN - 2052-4986
DOI - 10.1112/tlms/tlv002
Subject(s) - hermitian matrix , mathematics , dirac operator , pure mathematics , operator theory , clifford analysis , triple system , operator (biology) , algebra over a field , dirac (video compression format) , hermitian symmetric space , compact operator , mathematical physics , hermitian manifold , physics , quantum mechanics , computer science , geometry , chemistry , ricci curvature , biochemistry , curvature , repressor , transcription factor , neutrino , extension (predicate logic) , gene , programming language
The Dolbeault complex of a quantized compact Hermitian symmetric space is expressed in terms of the Koszul complex of a braided symmetric algebra of Berenstein and Zwicknagl. This defines a spectral triple quan‐tizing the Dolbeault–Dirac operator associated to the canonical spin cstructure.