A.D. Bell: Abstract

Skew differential operators on commutative rings


Allen D. Bell

Publication Information

Appeared in Abelian Groups and Noncommutative Rings: A collection of papers in memory of Robert B. Warfield, Jr., ed. L. Fuchs, K. R. Goodearl, J. T. Stafford, and C. Vinsonhaler, Contemporary Mathematics 130, American Mathematical Society, Providence, 1992, pp. 49-67
Math Reviews: 93h:13024

Abstract (in LaTex)

We define a ring of skew differential operators on a commutative
ring $A$ using a commutator twisted via the powers of an
automorphism $\phi$ of $A$, derive some of the basic properties
of this construction, and work out some examples.  We show that
many of the standard properties of differential operators
continue to hold with our definition but that a crucial
difference occurs for automorphisms of infinite order:
frequently the action of a skew differential operator is then
determined by its action on the powers of a single element of $A$.

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