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Hopf algebras with and without modular pairs in involution

date
13.11.2018 
time
03:00 PM - 04:00 PM 
speaker
Sebastian Halbig  
affiliation
TU Dresden, Institut für Geometrie 
language
en 
main topic
Mathematics: general
host
Prof. Dr. A. Thom  
abstract

A modular pair in involution of a Hopf algebra H is a pair consisting of a grouplike element g in H and a character f on H such that f(g) = 1 and the antipode square is given by the adjoint action of g and f. The ground field k of H can be viewed as a module and a comodule via the character and the grouplike, respectively. The module comodule k is then a stable anti-Yetter-Drinfeld module playing the role of coefficients in Hopf-cyclic cohomology introduced by Connes and Moscovici. When H is finite dimensional, the aforementioned antipode condition for (g,f) is a square root of the celebrated Radford formula for the 4th power of the antipode, and is thus related to the work of Radford and Kauffman concerning the existence of a ribbon element in the Drinfeld double of H.
Using Radford's biproduct (also known as Majid's bosonization) of certain Nichols algebras over cyclic groups, we construct finite-dimensional Hopf algebras that do not admit a modular pair in involution.
Based on joint work with U. Kraehmer.

 

Last update: 09.11.2018 08:59.

venue 

TUD Willers-Bau (WIL A 120) 
Zellescher Weg 12-14
01069 Dresden
homepage
https://navigator.tu-dresden.de/etplan/wil/00 

organizer 

TUD Mathematik
Willersbau, Zellescher Weg 12-14
01069 Dresden
telefon
49-351-463 33376 
homepage
http://tu-dresden.de/mathematik 
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