Formal confluence of quantum differential operators

Confluence Operators (JELIA'08)

In the logic based framework of knowledge representation and reasoning many operators have been defined in order to capture different kinds of change: revision, update, merging and many others. There are close links between revision, update, and merging. Merging operators can be considered as extensions of revision operators to multiple belief bases. And update operators can be considered as po...

Remarks on Quantum Differential Operators

In the course of writing the book [9] and various papers [10, 11, 12, 13, 14, 15, 16] we encountered many q-differential equations but were frustrated by a lack of understanding about natural forms for such equations. One has operators of the type qKP or qKdV for example but even there, expressing the resulting equations (even via Hirota type equations or in bilinear form) seemed curiously diff...

On a ring of formal pseudo-differential operators

Quantum Differential Operators on K[x]

Following the definition of quantum differential operators given in [LR1], we show that the ring of quantum differential operators on the affine line is the ring generated by x and ∂, the familiar differential operators on the line, along with two additional operators which we call ∂ 1 and ∂ −1 . We describe this ring both as a subring of the ring of graded endomorphisms and as a ring given by ...

0 Quantum Differential Operators on the Quantum Plane

The universal enveloping algebra U (G) of a Lie algebra G acts on its representation ring R through D(R), the ring of differential operators on R. A quantised universal enveloping algebra (or quantum group) is a deformation of a universal enveloping algebra and acts not through the differential operators of its representation ring but through the quantised differential operators of its represen...