Projective Quantum Modules and Projective Ideals of C*-algebras

  • A. Ya. Helemskii
Conference paper
Part of the Operator Theory: Advances and Applications book series (OT, volume 262)


We introduce in non-coordinate presentation the notions of a quantum algebra and of a quantum module over such an algebra. Then we give the definition of a projective quantum module and of a free quantum module, the latter as a particular case of the notion of a free object in a rigged category. (Here we say “quantum” instead of frequently used protean adjective “operator”). After this we discuss the general connection between projectivity and freeness.


Quantum algebra C*-algebras ideal quantum module projective object freeness 


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Faculty of Mechanics and MathematicsMoscow State (Lomonosov) UniversityMoscowRussia

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