Results 1 to 10 of about 2,471 (100)
Distinguished Pre-Nichols algebras [PDF]
Transformation Groups, 2014 We formally define and study the distinguished pre-Nichols algebra $\widetilde{\mathcal{B}}(V)$ of a braided vector space of diagonal type $V$ with finite-dimensional Nichols algebra $\mathcal{B}(V)$. The algebra $\widetilde{\mathcal{B}}(V)$ is presented
Angiono, Ivan
core +4 more sources
On finite dimensional Nichols algebras of diagonal type
Bulletin of Mathematical Sciences, 2017 This is a survey on Nichols algebras of diagonal type with finite dimension, or more generally with arithmetic root system. The knowledge of these algebras is the cornerstone of the classification program of pointed Hopf algebras with finite dimension ...
Nicolás Andruskiewitsch, Iván Angiono
doaj +3 more sources
Nichols Algebras of Unidentified Diagonal Type [PDF]
Communications in Algebra, 2013 20 ...
Iván Angiono
openaire +5 more sources
On Nichols (braided) Lie algebras [PDF]
International Journal of Mathematics, 2015 We prove {\rm (i)} Nichols algebra $\mathfrak B(V)$ of vector space $V$ is finite-dimensional if and only if Nichols braided Lie algebra $\mathfrak L(V)$ is finite-dimensional; {\rm (ii)} If the rank of connected $V$ is $2$ and $\mathfrak B(V)$ is an ...
Wu, Weicai +2 more
core +3 more sources
Factorization of Graded Traces on Nichols Algebras [PDF]
Axioms, 2017 A ubiquitous observation for finite-dimensional Nichols algebras is that as a graded algebra the Hilbert series factorizes into cyclotomic polynomials. For Nichols algebras of diagonal type (e.g., Borel parts of quantum groups), this is a consequence of ...
Simon Lentner, Andreas Lochmann
doaj +3 more sources
Relationship between Nichols braided Lie algebras and Nichols algebras
, 2014 We establish the relationship among Nichols algebras, Nichols braided Lie algebras and Nichols Lie algebras. We prove two results: (i) Nichols algebra $\mathfrak B(V)$ is finite-dimensional if and only if Nichols braided Lie algebra $\mathfrak L(V)$ is ...
Wu, Weicai +2 more
core +3 more sources
Geometric perspective on Nichols algebras
Journal of Algebra, 2022 We formulate the generation of finite dimensional pointed Hopf algebras by group-like elements and skew-primitives in geometric terms. This is done through a more general study of connected and coconnected Hopf algebras inside a braided fusion category $\mathcal{C}$.
Ehud Meir
openaire +5 more sources
Nichols algebras and Hecke-type Nichols sub-algebras(Nichols代数及其Hecke型子代数)
Zhejiang Daxue xuebao. Lixue ban, 2005 对Nichols代数，给出了它的Hecke型Nichols子代数的定义.在范畴中，H为群代数时，给出(V，c)是Hecke型的充要条件.设A=T(V)/IV是一个代数，讨论了IV成为余理想的条件.计算了二维对角型向量空间的二次Hopf代数，并且找出了一些Nichols代数.
WANGYan(王燕)
doaj +2 more sources
On the Lifting of Nichols Algebras [PDF]
Communications in Algebra, 2012 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.
openaire +4 more sources
On Nichols algebras over SL(2,Fq) and GL(2,Fq) [PDF]
Journal of Mathematical Physics, 2007 We compute necessary conditions on Yetter-Drinfeld modules over the groups SL(2,Fq) and GL(2,Fq) to generate finite dimensional Nichols algebras.
Andruskiewitsch N. +7 more
core +7 more sources