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Regular Algebras Related To Regular Graded Skew Clifford Algebras Of Low Global Dimension

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Regular Algebras Related To Regular Graded Skew Clifford Algebras Of Low Global Dimension

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dc.contributor.author Nafari, Manizheh en_US
dc.date.accessioned 2011-10-11T20:49:03Z
dc.date.available 2011-10-11T20:49:03Z
dc.date.issued 2011-10-11
dc.date.submitted January 2011 en_US
dc.identifier.other DISS-11335 en_US
dc.identifier.uri http://hdl.handle.net/10106/6190
dc.description.abstract M. Artin, W. Schelter, J. Tate, and M. Van den Bergh introduced the notion of non-commutative regular algebras, and classified regular algebras of global dimension 3 on degree-one generators by using geometry (i.e., point schemes) in the late 1980s. Recently, T. Cassidy and M. Vancliff generalized the notion of a graded Clifford algebra and called it a graded skew Clifford algebra.In this thesis, we prove that all classes of quadratic regular algebras of global dimension 3 contain graded skew Clifford algebras or Ore extensions of graded skew Clifford algebras of global dimension 2. We also prove that some regular algebras of global dimension 4 can be obtained from Ore extensions of regular graded skew Clifford algebras of global dimension 3. We also show that a certain subalgebra R of a regular graded skew Clifford algebra A is a twist of the polynomial ring if A is a twist of a regular graded Clifford algebra B. We have an example that demonstrates that this can fail when A is not a twist of B. en_US
dc.description.sponsorship Vancliff, Michaela en_US
dc.language.iso en en_US
dc.publisher Mathematics en_US
dc.title Regular Algebras Related To Regular Graded Skew Clifford Algebras Of Low Global Dimension en_US
dc.type Ph.D. en_US
dc.contributor.committeeChair Vancliff, Michaela en_US
dc.degree.department Mathematics en_US
dc.degree.discipline Mathematics en_US
dc.degree.grantor University of Texas at Arlington en_US
dc.degree.level doctoral en_US
dc.degree.name Ph.D. en_US

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