TY  - JOUR
U1  - Wissenschaftlicher Artikel
A1  - Helbig, Michael
T1  - On the Lifting of Nichols Algebras
JF  - Communications in Algebra
N2  - Nichols algebras are a fundamental building block of pointed Hopf algebras. Part of the classification program of finite-dimensional pointed Hopf algebras with the lifting method of Andruskiewitsch and Schneider is the determination of the liftings, i.e., all possible deformations of a given Nichols algebra. Based on recent work of Heckenberger about Nichols algebras of diagonal type we compute explicitly the liftings of all Nichols algebras with generalized Cartan matrix of type A 2, some Nichols algebras with generalized Cartan matrix of type B 2, and some Nichols algebras of two Weyl equivalence classes of non-standard type
giving new classes of finite-dimensional pointed Hopf algebras.
AB  - Nichols algebras are a fundamental building block of pointed Hopf algebras. Part of the classification program of finite-dimensional pointed Hopf algebras with the lifting method of Andruskiewitsch and Schneider is the determination of the liftings, i.e., all possible deformations of a given Nichols algebra. Based on recent work of Heckenberger about Nichols algebras of diagonal type we compute explicitly the liftings of all Nichols algebras with generalized Cartan matrix of type A 2, some Nichols algebras with generalized Cartan matrix of type B 2, and some Nichols algebras of two Weyl equivalence classes of non-standard type
giving new classes of finite-dimensional pointed Hopf algebras.
Y1  - 2012
U6  - https://doi.org/10.1080/00927872.2011.568029
DO  - https://doi.org/10.1080/00927872.2011.568029
VL  - 40
IS  - 9
SP  - 3317
EP  - 3351
S1  - 35
PB  - Informa UK Limited
ER  -