Abstract
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.
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Helemskii, A.Y. (2018). Projective Quantum Modules and Projective Ideals of C*-algebras. In: Duduchava, R., Kaashoek, M., Vasilevski, N., Vinnikov, V. (eds) Operator Theory in Different Settings and Related Applications. Operator Theory: Advances and Applications, vol 262. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-62527-0_6
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DOI: https://doi.org/10.1007/978-3-319-62527-0_6
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-62526-3
Online ISBN: 978-3-319-62527-0
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