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Full-Text Articles in Algebra
Π-Operators In Clifford Analysis And Its Applications, Wanqing Cheng
Π-Operators In Clifford Analysis And Its Applications, Wanqing Cheng
Graduate Theses and Dissertations
In this dissertation, we studies Π-operators in different spaces using Clifford algebras. This approach generalizes the Π-operator theory on the complex plane to higher dimensional spaces. It also allows us to investigate the existence of the solutions to Beltrami equations in different spaces.
Motivated by the form of the Π-operator on the complex plane, we first construct a Π-operator on a general Clifford-Hilbert module. It is shown that this operator is an L^2 isometry. Further, this can also be used for solving certain Beltrami equations when the Hilbert space is the L^2 space of a measure space. This idea is …
On Rings Of Invariants For Cyclic P-Groups, Daniel Juda
On Rings Of Invariants For Cyclic P-Groups, Daniel Juda
Graduate Theses and Dissertations
This thesis studies the ring of invariants R^G of a cyclic p-group G acting on k[x_1,\ldots, x_n] where k is a field of characteristic p >0. We consider when R^G is Cohen-Macaulay and give an explicit computation of the depth of R^G. Using representation theory and a result of Nakajima, we demonstrate that R^G is a unique factorization domain and consequently quasi-Gorenstein. We answer the question of when R^G is F-rational and when R^G is F-regular.
We also study the a-invariant for a graded ring S, that is, the maximal graded degree of the top local cohomology module of S. …