Invariants du corps de weyl sous l'action de groupes finis

Some aspects of noncommutative invariant theory and the Noether’s problem

“…Also, the k i 's must be chosen in a way that k i+1 = Frac k i [x, α, δ], a skew-field of an Ore extension. In this way, a generalization of the Miyata's Theorem [38] for polynomial extensions can be used: [3] Let K be a field (commutative or not), α an automorphism and δ a α-derivation of K . Let S = K [x, α, δ] be an Ore extension, with skew-field of fractions D. Let G be a subgroup of ring automorphisms of S, not necesserely finite, such that G(K ) ⊆ K .…”

Injective Hulls of Simple Modules over Differential Operator Rings

“…Then is isomorphic to one of the following algebras: K[x, y], a quantum plane, a quantum Weyl algebra or to a differential operator ring. Since any automorphism of K[x] is such that σ(x) = qx + b for some q, b ∈ K, following the proof of [2] and [1], we have:…”

“…This extends a recent result by I.Musson for the derivations d(x) = x r (see [20]). Applying a result of P.Carvalho and I.Musson [5] and results of Alev et al [1] and Awami et al [2], we can also characterise those Ore extensions of K[x] which satisfy (⋄).…”

Rigidity of graded regular algebras

“…Notice that g induces an automorphism of C x, y −1 = A 1 (C), so that by [AD2], This paper gives a number of algebras where A G is never isomorphic to A, so it would be interesting to determine (a) when Q(A) G is isomorphic to Q(A), and (b) when Q (A) G is isomorphic to Q(B) for an Artin-Schelter regular algebra B.…”

“…(and for any finite group with n = 1, see [AD2]). One could investigate similar questions for the quotient division algebras of Artin-Schelter regular algebras.…”