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

2015/01/19 by Nicolás Andruskiewitsch, Andruskiewitsch, Nicolás, Iván Angiono +3 · 1 citation
Mathematics · Physics and Astronomy · #16W30 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1501.04518

openalex publication_date 2015/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \B_ mathfrakq be a finite-dimensional Nichols algebra of\ndiagonal type corresponding to a matrix mathfrakq. We consider the graded\ndual \L_ mathfrakq of the distinguished pre-Nichols algebra\n widetilde\B_ mathfrakq from [A3] and the divided powers\nalgebra \U_ mathfrakq, a suitable Drinfeld double of\n\L_ mathfrakq # \k \ℤ^\θ. We provide basis\nand presentations by generators and relations of \L_ mathfrakq\nand \U_ mathfrakq, and prove that they are noetherian and have\nfinite Gelfand-Kirillov dimension.\n

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