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UBC Theses and Dissertations

Representation theory of variety of algebras Lee, Hei-Sook


While there is considerable literature about algebras satisfying a polynomial identity, there are only scant results about varieties of algebras. For such an algebra we can introduce the notions of bimodule, birepresentation and universal enveloping algebra as an extension of the notions of module and representation for associative algebras. Moreover, it is possible to define injective hulls for these restricted representations. We derive a rather concrete structure theorem of I-bimodules M for a finite dimensional algebra in a certain variety by studying a universal enveloping algebra and injective hulls.

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