Topology-preserving quantum deformation with non-numerical parameter

21st International Conference on Integrable Systems and Quantum Symmetries

Aukhadiev, Marat^1 ; Grigoryan, Suren^1 ; Lipacheva, Ekaterina^1

Kazan State Power Engineering University, Krasnoselskaya 51, Kazan, 420066, Russia^1

关键词: Numerical parameters;    Projective spaces;    Quantum deformation;    Quotient groups;    Semi-group;    Semigroups;    Topology preserving;    Weak hopf algebras;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/474/1/012007/pdf
DOI  :  10.1088/1742-6596/474/1/012007

来源: IOP

【 摘 要 】

We introduce a class of compact quantum semigroups, that we call semigroup deformations of compact Abelian qroups. These objects arise from reduced semigroup C*-algebras, the generalization of the Toeplitz algebra. We study quantum subgroups, quantum projective spaces and quantum quotient groups for such objects, and show that the group is contained as a compact quantum subgroup in the deformation of itself. The connection with the weak Hopf algebra notion is described. We give a grading on the C*-algebra of the compact quantum semigroups constructed.