2007/04/06 by Heidi Haynal, Haynal, Heidi
Mathematics · Physics and Astronomy · #16P40 #16R99 #16S36 #81R50 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Rings and Algebras (math.RA) #math.QA #math.RA #msc:16P40 #msc:16R99 #msc:16S36 #msc:81R50
paper · pdf · doi:10.48550/arxiv.0704.0846
43 pages; Submitted to the Journal of Algebra
arxiv created 2007/04/06 · openalex publication_date 2007/04/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For k a field of arbitrary characteristic, and R a k-algebra, we show that the PI degree of an iterated skew polynomial ring R[x1;τ1,δ1]...b[xn;τn,δn] agrees with the PI degree of R[x1;τ1]...b[xn;τn] when each (τi,δi) satisfies a qi-skew relation for qi ∈ k× and extends to a higher qi-skew τi-derivation. We confirm the quantum Gel'fand-Kirillov conjecture for various quantized coordinate rings, and calculate their PI degrees. We extend these results to completely prime factor algebras.