List of finite-dimensional Nichols algebras

In mathematics, a Nichols algebra is a Hopf algebra in a braided category assigned to an object V in this category (e.g. a braided vector space). The Nichols algebra is a quotient of the tensor algebra of V enjoying a certain universal property and is typically infinite-dimensional. Nichols algebras appear naturally in any pointed Hopf algebra and enabled their classification in important cases. The most well known examples for Nichols algebras are the Borel parts ${\displaystyle U_{q}({\mathfrak {g}})^{+}}$ of the infinite-dimensional quantum groups when q is no root of unity, and the first examples of finite-dimensional Nichols algebras are the Borel parts ${\displaystyle u_{q}({\mathfrak {g}})^{+}}$ of the Frobenius–Lusztig kernel (small quantum group) when q is a root of unity.

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