Symmetry/Asymmetry Study in Hopf-Type Algebras and Groups
A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".
Deadline for manuscript submissions: closed (15 February 2024) | Viewed by 475
Special Issue Editor
Special Issue Information
Dear Colleagues,
Noncommutative geometry is used to deal with noncommutative algebras, which are the algebras of functions on “noncommutative spaces” such as groups, groupoids and quasigroups. Noncommutative geometry can be used to express notions, structures, and techniques useful in handling usual geometric spaces in terms of the algebra of functions including symmetry and asymmetry, 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 noncommutative Hopf algebra or quantum group.
Generalisations of Hopf algebras have quite a long history. To date, there are two classes. One is that such generalisations are the changing of some of the algebraic conditions that enter the definition of a Hopf algebra. A few examples include weak Hopf algebras, quasi Hopf algebras, Hopf group-coalgebras , hom-Hopf algebras and Hopf quasigroups. The other is that when we consider the functional algebras on an infinite group or a groupoid we have the theory of multiplier Hopf algebra or the theory of weak multiplier Hopf algebra.
Prof. Dr. Shuanhong Wang
Guest Editor
Manuscript Submission Information
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Keywords
- Hopf algebra and multiplier Hopf algebra
- quantum group
- Hopf group coalgebra
- braided tensor category
- groupoid
- quasigroup
- algebra
- coalgebra
- Yang–Baxter equation
- linear algebra
- braided Lie algebra
- group
- duality
