On the Hopf algebra structure of the Lusztig quantum divided power\n algebras

2020/05/17 by Nicolás Andruskiewitsch, Andruskiewitsch, Nicolás, Iván Angiono +3
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.2005.08342

openalex publication_date 2020/05/17 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

We study the Hopf algebra structure of Lusztig's quantum groups. First we\nshow that the zero part is the tensor product of the group algebra of a finite\nabelian group with the enveloping algebra of an abelian Lie algebra. Second we\nbuild them from the plus, minus and zero parts by means of suitable actions and\ncoactions within the formalism presented by Sommerhauser to describe triangular\ndecompositions.\n

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