Hopf-Type Algebras, Lie Algebras, Quantum Groups and Related Topics
A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematical Physics".
Deadline for manuscript submissions: closed (31 December 2023) | Viewed by 13011
Special Issue Editor
Special Issue Information
Dear Colleagues,
Generally, the idea of noncommutative geometry is to deal with noncommutative algebras which are the algebras of functions on some “noncommutative space”, such as groups, groupoids, and quasigroups. Noncommutative geometry finds to express notions, structures, and techniques useful in handling usual geometric spaces in terms of the algebra of functions, and then to generalize them to the noncommutative setting. A structure which has been successfully generalized in that way is that of a group, resulting in the notion of a noncommutative and non-cocommutative Hopf algebra or quantum group.
Generalizations of Hopf algebras have quite a long history. Up to now, there are the following two classes. One is that such generalizations are the changing of some of the algebraic conditions that enter the definition of a Hopf algebra. We mention here but a few examples: weak Hopf algebras, quasi Hopf algebras, Hopf group-coalgebras, hom-Hopf algebras and Hopf quasigroups. These objects were related to braided monoidal categories and Yang–Baxter equation and so on. The other is that when we consider the functional algebras on an infinite group or a groupoid we had the theory of multiplier Hopf algebra or the theory of weak multiplier Hopf algebra.
Prof. Dr. Shuanhong Wang
Guest Editor
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Keywords
- topics related to Hopf algebras, (weak) multiplier Hopf algebras, quantum groups, Hopf group-coalgebras, hom-Hopf algebras, quasi Hopf algebras, Hopf quasigroups
- braided monoidal categories, fusion categories, braided crossed categories, groupoids, Yang–Baxter equation
- algebras, coalgebras, symmetry, duality, differential calculi, (co)homologies
- braided lie algebras, lie coalgebras
- applications of above topics
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