Twisted Hopf Algebras, Ringel–Hall Algebras, and Green's Categories: With an appendix by the referee
✍ Scribed by Libin Li; Pu Zhang
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 215 KB
- Volume
- 231
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
✦ Synopsis
The concept and some basic properties of a twisted Hopf algebra are introduced and investigated. Its unique difference from a Hopf algebra is that the comultiplication ␦ : A ª A m A is an algebra homomorphism, not for the componentwise multiplication on A m A, but for the twisted multiplication on A m A given by Lusztig's rule.
Also, it is proved that any object A in Green's category has a twisted Hopf algebra structure, any morphism between objects is a twisted Hopf algebra homo-Ž . morphism, the antipode s of A is self-adjoint under the Lusztig form y, y on A, Ž . and the Green polynomials M t share a so-called cyclic-symmetry.
a, b