PI degree parity in q-skew polynomial rings
Abstract
Description
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[x_1;τ_1,δ_1]...b[x_n;τ_n,δ_n] agrees with the PI degree of R[x_1;τ_1]...b[x_n;τ_n] when each (τ_i,δ_i) satisfies a q_i-skew relation for q_i \in k^{\times} and extends to a higher q_i-skew τ_i-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.
43 pages; Submitted to the Journal of Algebra
43 pages; Submitted to the Journal of Algebra