Oberseminar
zur
Algebra und Algebraischen Kombinatorik
Dr. Tobias Ohrmann
(Leibniz Universität Hannover)
Higher braidings of diagonal type
To a braided vector space(V; c)we can associate a Hopf algebraB(V) =T(V)=I, where
the idealIcan be defined as the kernel of a certain symmetrizer map associated to the
braidingc:VV!VV. The Hopf algebraB(V)is known as the Nichols algebra of
(V; c). Given a generalized Cartan matrixAof finite type and a parameterq2C

, it
is well-known that the positive part of the Drinfeld-Jimbo quantum enveloping algebra
Uq(A)is a Nichols algebra. On the other hand, given a braided vector space(V; c)of
diagonal type, under certain conditions we can associate to its Nichols algebraB(V)a so-
called Weyl groupoid, which can be seen as a generalization of an ordinary Weyl group.
However, the correspondence between Nichols algebras and Weyl groups/groupoids is
far from being bijective and there are indications that one needs to replace braided
vector spaces by higher braided structures in order to improve it. In the talk, we want
to introduce these structures and discuss the aforementioned indications.
This is joint work with Michael Cuntz.
Montag 20.12.2021
ab 14:15 Uhr,in StudIP, per BBB im e-a410
Alle Interessierten sind herzlich eingeladen.
Institut für Algebra, Zahlentheorie
und Diskrete Mathematik