Distinguished Pre-Nichols algebras

IVÁN ANGIONO

TRANSFORMATION GROUPS

BIRKHAUSER BOSTON INC

Año: 2016 vol. 21 p. 1 - 33

1083-4362

We formally define and study the distinguished pre-Nichols algebra B?(V) of a braided vector space of diagonal type V with finite-dimensional Nichols algebra B(V). The algebra B?(V) is presented by fewer relations than B(V), so it is intermediate between the tensor algebra T(V) and B(V). Prominent examples of distinguished pre-Nichols algebras are the positive parts of quantized enveloping (super)algebras and their multiparametric versions. We prove that these algebras give rise to new examples of Noetherian pointed Hopf algebras of finite Gelfand-Kirillov dimension. We investigate the kernel (in the sense of Hopf algebras) of the projection from B?(V) to B(V), generalizing results of De Concini and Procesi on quantum groups at roots of unity.