Effacement des dérivations et spectres premiers des algèbres quantiques |
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Authors: | Grard Cauchon |
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Institution: | Laboratoire d'équations aux dérivées partielles et physique mathématique, UMR CNRS 6056, UFR Sciences, BP 1039, 51687, Reims cedex 2, France |
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Abstract: | Given any (commutative) field k and any iterated Ore extension R=kX1]X2;σ2,δ2]XN;σN,δN] satisfying some suitable assumptions, we construct the so-called “Derivative-Elimination Algorithm.” It consists of a sequence of changes of variables inside the division ring F=Fract(R), starting with the indeterminates (X1,…,XN) and terminating with new variables (T1,…,TN). These new variables generate some quantum-affine space
such that
. This algorithm induces a natural embedding
which satisfies the following property: . We study both the derivative-elimination algorithm and natural embedding and use them to produce, for the general case, a (common) proof of the “quantum Gelfand–Kirillov” property for the prime homomorphic images of the following quantum algebras:
,
(wW), RqG] (where G denotes any complex, semi-simple, connected, simply connected Lie group with associated Lie algebra
and Weyl group W), quantum matrices algebras, quantum Weyl algebras and quantum Euclidean (respectively symplectic) spaces. Another application will be given in G. Cauchon, J. Algebra, to appear]: In the general case, the prime spectrum of any quantum matrices algebra satisfies the normal separation property. |
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