We give a projective resolution of a finite dimensional π«-algebra π¬ over its enveloping algebra π¬<SUP>π</SUP> = π¬<SUP>ππ</SUP> β¨<SUB>π«</SUB>π¬. The description of this resolution is related to decompositions of the first syzygy module of π¬ as an π¬<SUP>π</SUP> module. Resolutions of right π¬ modules π<SUB>π¬</SUB> may be obtained by tensoring π over π¬ with this bimodule resoution. We describe how to obtain such a resolution when π is simple or when π is given in the form of a projective presentation. Computations of <I>πΈπ₯π‘</I><SUB>π¬</SUB><SUP>π</SUP>(π<SUB>π£</SUB>,π<SUB>π€</SUB>) for certain classes of algebras π¬ are made using these resolutions, and applied to obtain results on global dimension. / Ph. D.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/37649 |
| Date | 24 April 1999 |
| Creators | Smith, Nathan A. |
| Contributors | Mathematics, Green, Edward L., Haskell, Peter E., Linnell, Peter A., Rossi, John F., Thomson, James E. |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Detected Language | English |
| Type | Dissertation |
| Format | application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
| Relation | etd.pdf |
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