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Let G ≤ SLn+1(C) act on R = C[X1, ..., Xn+1] by change of variables. Then, the skew-group algebra R*G is bimodule (n+1)-Calabi-Yau. In certain circumstances, this algebra admits a locally finite-dimensional grading of Gorenstein parameter 1, in which case it is the (n+1)-preprojective algebra of its n-representation infinite degree 0 piece. If the group G is abelian, the (n+1)-preprojective algebra is said to be of type Ã. For a given group G, it is not obvious whether R*G admits such a grading making it into an (n+1)-preprojective algebra. We study the case when n=2 and G is abelian. We give an explicit classification of groups such that R*G is 3-preprojective by constructing such gradings. This is possible as long as G is not a subgroup of SL2(C) and not C2 x C2. For a fixed G, the algebra R*G admits different 3-preprojective gradings, so we associate a type to a grading and classify all types. Then we show that gradings of the same type are related by a certain kind of mutation. This gives a classification of 2-representation infinite algebras of type Ã. The involved quivers are those arising from hexagonal dimer models on the torus, and the gradings we consider correspond to perfect matchings on the dimer, or equivalently to periodic lozenge tilings of the plane. Consequently, we classify these tilings up to flips, which correspond to the mutation we consider. / <p>Oleksandra Gasanova, Universität Duisburg-Essen, is co-author of the included work</p>

The primary purpose of this paper is to state a set of postulates for Boolean algebra and show the characteristic theorems derivable from them, and to unify in one paper the more important methods of representing Boolean algebra and show their equivalence.

Thesis (D.A.)--Illinois State University, 1983. / Title from title page screen, viewed May 11, 2005. Dissertation Committee: Albert D. Otto (chair), John A. Dossey, Kenneth A. Retzer, Linnea L. Sennott, Seth F. Carmody. Includes bibliographical references (leaves 27-28) and abstract. Also available in print.

Thesis (Ph.D.)--Ohio University, June, 2005. / Title from PDF t.p. Includes bibliographical references (p. 65-69)

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