classification of the finite dimensional, indecomposable representations of the Euclidean algebra e (2) having two generators.
Published: 2006
Language: eng
Number of pages: 147
ISBN-13: 9780494160169
Description: The Euclidean algebra   e (2) is the Lie algebra of the group E(2) of Euclidean transformations of the plane. This thesis examines the finite dimensional representations of   e (2) having two generators. Given a representation with a fixed pair of generators we associate a graph: the graph is dependent on the choice of generators and for each isomorphism class of representations there are infinitely many possible graphs. In term of graphs, we give a criterion for the indecomposability of such representations and describe an invariant for the indecomposable representations.Next, we classify the finite dimensional, indecomposable representations of   e (2) having two generators. We describe a procedure that enables us to select a single graph for each isomorphism class. This graph uniquely identifies the class.
Notes: Source: Dissertation Abstracts International, Volume: 67-07, Section: B, page: 3832.

Thesis (Ph.D.)--University of Toronto, 2006.

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