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Virginia Tech

Syzygy Decompositions and Projective Resolutions

Abstract

dc:description.abstract

We give a projective resolution of a finite dimensional 𝛫-algebra 𝛬 over its enveloping algebra 𝛬<SUP>𝑒</SUP> = 𝛬<SUP>π‘œπ‘</SUP> ⨂<SUB>𝛫</SUB>𝛬. The description of this resolution is related to decompositions of the first syzygy module of 𝛬 as an 𝛬<SUP>𝑒</SUP> module. Resolutions of right 𝛬 modules 𝑀<SUB>𝛬</SUB> may be obtained by tensoring 𝑀 over 𝛬 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 <I>𝐸π‘₯𝑑</I><SUB>𝛬</SUB><SUP>𝑛</SUP>(𝑆<SUB>𝑣</SUB>,𝑆<SUB>𝑀</SUB>) for certain classes of algebras 𝛬 are made using these resolutions, and applied to obtain results on global dimension.

Degree

thesis:*
Name thesis:degree_name
Ph. D.
Level thesis:degree_level
doctoral
Discipline thesis:degree_discipline
Mathematics
Department dc:contributor.department
Mathematics
Grantor dc:publisher
Virginia Tech
Year dc:date.issued
1999

Author and committee

dc:creator, dc:contributor.*
Author dc:creator
  • Smith, Nathan A.
Chair dc:contributor.committeechair
  • Green, Edward L.
Committee members dc:contributor.committeemember
  • Haskell, Peter E.
  • Linnell, Peter A.
  • Rossi, John F.
  • Thomson, James E.

Subjects

dc:subject × 6

Rights

dc:rights
Statement dc:rights
  • In Copyright

Identifiers

dc:identifier.*
Dc Identifier Other
etd-042199-120414
OAI identifier oai:identifier
oai:vtechworks.lib.vt.edu:10919/37649

Chain of custody

source
Harvested from
Virginia Tech
Base URL
vtechworks.lib.vt.edu/oai/request
Last updated
2026-07-22
Source record
OAI-PMH GetRecord
citation

Smith, Nathan A.. Syzygy Decompositions and Projective Resolutions. doctoral thesis, Virginia Tech, 1999. http://hdl.handle.net/10919/37649