Global and Krull Dimensions of Quantum Weyl Algebras

✍ Scribed by Hisaaki Fujita; Ellen Kirkman; James Kuzmanovich

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 511 KB
• Volume: 216
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.1998.7790

✦ Synopsis

Giaquinto and J. Zhang defined a natural quantization An(R) of the nth Weyl algebra A n based on R and studied many ring theoretic properties of rings A2(Ja, b) (arising from the "Jordan" Hecke symmetry) and An(q, Pi,j) (arising from the standard multiparameter Hecke symmetry). Here we compute the global and Krull dimensions in the cases that were left open; namely, we show that over any field k of characteristic zero, gldim(A2(Ja,b)) = Kdim(A2(Ja, b)) = 3 for any a, b ~k with a v~ b, and gldim(An(+_l, pi, y))= Kdim(An(_+ 1, Pi,j)) = n.