PI degree parity in q-skew polynomial rings

Details PI degree parity in q-skew polynomial rings PI degree parity in q-skew polynomial rings

2007-04-06

arxiv.org/abs/0704.0846v1

Mathematics

Rings and Algebras

43 pages; Submitted to the Journal of Algebra

Scientific paper

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;\tau_1,\delta_1]...b[x_n;\tau_n,\delta_n] agrees with the PI degree of R[x_1;\tau_1]...b[x_n;\tau_n] when each (\tau_i,\delta_i) satisfies a q_i-skew relation for q_i \in k^{\times} and extends to a higher q_i-skew \tau_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.

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