Nichols algebras with standard braiding

Lifting of Nichols Algebras of Type B 2 ∗

We compute liftings of the Nichols algebra of a Yetter-Drinfeld module of Cartan type B2 subject to the small restriction that the diagonal elements of the braiding matrix are primitive nth roots of 1 with odd n 6= 5. As well, we compute the liftings of a Nichols algebra of Cartan type A2 if the diagonal elements of the braiding matrix are cube roots of 1; this case was not completely covered i...

1 7 M ar 2 00 4 Nichols algebras of U q ( g ) - modules ⋆

A technique is developed to reduce the investigation of Nichols algebras of integrable Uq(g)-modules to the investigation of Nichols algebras of braided vector spaces with diagonal braiding. The results are applied to obtain information on the Gelfan’dKirillov dimension of these Nichols algebras and their defining relations if the braiding is of a special type and q is not a root of unity. For ...

Multiplicative bijective maps on standard operator algebras

Braiding With Majorana Fermions

This paper is an introduction to relationships between topology, quantum computing and the properties of fermions. In particular we study the remarkable unitary braid group representations associated with Majorana fermions.

Classification of Quiver Hopf Algebras and Pointed Hopf Algebras of Nichols Type

The quiver Hopf algebras are classified by means of ramification system with irreducible representations. This leads to the classification of Nichols algebras over group algebras and pointed Nichols type Hopf algebras. 2000 Mathematics Subject Classification: 16W30, 16G10 keywords: Quiver, Hopf algebra, Hopf bimodule, Nichols algebras