2025/07/15 by Teodor Banica, Banica, Teo
Computer Science · #FOS: Mathematics #Quantum Algebra (math.QA) #Quantum Computing Algorithms and Architecture #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2507.11459
openalex publication_date 2025/07/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This is an introduction to quantum algebra, from a geometric perspective. The classical spaces X, such as the Lie groups, homogeneous spaces, or more general manifolds, are described by various algebras A, defined over various fields F. These algebras A satisfy a commutativity type condition, and the general idea is that of lifting this condition, and calling quantum spaces the underlying space-like objects X. One problem comes from the fact that different fields F lead, via different algebras A, to different classes of quantum spaces X. Our aim here is to identify and put at the center of the presentation those quantum spaces X which do not depend on the choice of F.