David A. Jordan

Isomorphism problems and groups of automorphisms for generalized Weyl algebras

We present solutions to isomorphism problems for various generalized Weyl algebras, including deformations of type-A Kleinian singularities and the algebras similar to U(sl2) introduced by S. P. Smith. For the former, we generalize results of Dixmier on the first Weyl algebra and the minimal primitive factors of U(sl2) by finding sets of generators for the group of automorphisms.

Finite-dimensional simple modules over certain iterated skew polynomial rings

We classify the finite-dimensional simple R-modules for a class of algebras which arise as iterated skew polynomial rings in two variables over commutative K-algebras for an algebraically closed field k of arbitrary characteristic. The class includes the enveloping algebra and the quantized enveloping algebra of the Lie algebra sl(2, k), the quantized Weyl algebra in two variables, various quantum groups, and the enveloping algebra of the dispin Lie superalgebra.

A note on semiprimitivity of ore extensions

A well known result on polynomial rings states that, for a given ring

Primitive Ore extensions

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The Graded Algebra Generated by Two Eulerian Derivatives

, if

Localizations of injective modules

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Poisson brackets and Poisson spectra in polynomial algebras

has no non-zero nil ideals then the polynomial ring

NORMAL ELEMENTS OF DEGREE ONE IN ORE EXTENSIONS

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ORE EXTENSIONS AND POISSON ALGEBRAS

(x) is semiprimitive, see for example (5) p.12. In this note we study Ore extensions of the form

The Lie ring of symmetric derivations of a ring with involution

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