A finite-dimensional Lie algebra arising from a Nichols algebra of diagonal type (rank 2)

2016/03/30 by Nicolás Andruskiewitsch, Andruskiewitsch, Nicolás, Iván Angiono +3
Chemistry · Mathematics · #16T20 (Secondary) #17B37 (Primary) #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Carbohydrate Chemistry and Synthesis #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA #msc:16T20 #msc:17B37

paper · pdf · doi:10.48550/arxiv.1603.09387

19 pages

arxiv created 2016/03/30 · openalex publication_date 2016/03/30 · arxiv updated 2016/04/01 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28

Abstract

Let B_\mathfrakq be a finite-dimensional Nichols algebra of diagonal type corresponding to a matrix \mathfrakq ∈ k^{θ× θ}, where k is an algebraically closed field of characteristic 0. Let L_\mathfrakq be the Lusztig algebra associated to B_\mathfrakq, see http://arxiv.org/abs/1501.04518. We present L_\mathfrakq as an extension (as braided Hopf algebras) of B_\mathfrakq by \mathfrak Z_\mathfrakq where \mathfrak Z_\mathfrakq is isomorphic to the universal enveloping algebra of a Lie algebra \mathfrak n_\mathfrakq. We compute the Lie algebra \mathfrak n_\mathfrakq when θ= 2.

Citations

• The quantum divided power algebra of a finite-dimensional Nichols algebra of diagonal type

Related

• Lie algebras arising from Nichols algebras of diagonal type
• Distinguished Pre-Nichols algebras
• Finite dimensional rank 2 Nichols algebras of diagonal type II: Classification
• On Finite dimensional Nichols algebras of diagonal type
• Lusztig isomorphisms for Drinfel'd doubles of bosonizations of Nichols algebras of diagonal type