Syzygy Decompositions and Projective Resolutions
Smith, Nathan A.
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We give a projective resolution of a finite dimensional K-algebra A over its enveloping algebra Ae = Aop Ã KA. The description of this resolution is related to decompositions of the first syzygy module of A as an Ae module. Resolutions of right A modules MA may be obtained by tensoring M over A with this bimodule resoution. We describe how to obtain such a resolution when M is simple or when M is given in the form of a projective presentation. Computations of ExtnA(Sv,Sw) for certain classes of algebras A are made using these resolutions, and applied to obtain results on global dimension.
- Doctoral Dissertations