Brauer groups of H-dimodule algebras and truncated power series Hopf algebras.
| dc.contributor.author | Tan, Richard Beng-tok, | en_US |
| dc.date.accessioned | 2013-08-16T12:28:00Z | |
| dc.date.available | 2013-08-16T12:28:00Z | |
| dc.date.issued | 1980 | en_US |
| dc.description.abstract | The Brauer group of H-dimodule algebras, BD(R, H), consists of equivalence classes of H-Azumaya algebras; where H is a Hopf algebra over a commutative ring R, and an H-dimodule algebra A is defined to be H-Azumaya if certain maps (analogous to the usual map A (CRTIMES) A (--->) End(A)) are isomorphisms. It is shown that if R is a separably closed field of characteristic p and H is a truncated power series Hopf algebra then a necessary and sufficient condition for an H-Azumaya algebra A to be R-Azumaya (the usual Azumaya R-algebra) is that it be semisimple. An example is given to show that semisimplicity is necessary for this to be true. | en_US |
| dc.description.abstract | BD(, 0)(R, H) is the subset of BD(R, H) consisting of only those H-Azumaya algebras that are already R-Azumaya. If each element {A} in BD(, 0)(R, H) has the property that A (TURNEQ) End(V) as an H-module algebra for some finitely generated projective H-module V, then BD(, 0)(R, H) is a subgroup of BD(R, H). For the truncated power series Hopf algebra (alpha)(, p) = k{x}/(x('p)), with x primitive, BD(, 0)(R, (alpha)(, p)) = R* when R is a perfect field of characteristic p and has trivial Brauer group. | en_US |
| dc.format.extent | 55 leaves : | en_US |
| dc.identifier.uri | http://hdl.handle.net/11244/4709 | |
| dc.note | Source: Dissertation Abstracts International, Volume: 41-02, Section: B, page: 0593. | en_US |
| dc.subject | Mathematics. | en_US |
| dc.thesis.degree | Ph.D. | en_US |
| dc.thesis.degreeDiscipline | Department of Mathematics | en_US |
| dc.title | Brauer groups of H-dimodule algebras and truncated power series Hopf algebras. | en_US |
| dc.type | Thesis | en_US |
| ou.group | College of Arts and Sciences::Department of Mathematics | |
| ou.identifier | (UMI)AAI8016935 | en_US |
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