Let k be an algebraically closed field of characteristic 0. This thesis develops techniques used to determine the structure of a finite dimensional Hopf algebra over k. The Hopf algebras of dimension $\leq$11 are classified. / Let p be a prime number, r a positive integer, and n = p$\sp{\rm r}-1$. Let GF(p$\sp{\rm r}$) be the Galois field of order p$\sp{\rm r}$. Let G = GF(p$\sp{\rm r}$) $\times$ $\sb\varphi$ GF(p$\sp{\rm r}$)$\sp\cdot$ be the semidirect product of GF(p$\sp{\rm r}$) and GF(p$\sp{\rm r}$)$\sp\cdot$ relative to the homomorphism $\varphi$:GF(p$\sp{\rm r}$)$\sp\cdot$ $\to$ AutGF(p$\sp{\rm r}$) defined by $\varphi$(x)(v) = xv for v$\in$ GF(p$\sp{\rm r}$) and x$\in$ GF(p$\sp{\rm r}$)$\sp\cdot$. A Hopf algebra H of dimension n$\sp2$(n + 1) is constructed which contains a Hopf subalgebra isomorphic to (kG)*. H is shown to be isomorphic to its linear dual. / Source: Dissertation Abstracts International, Volume: 50-02, Section: B, page: 0606. / Major Professor: Warren D. Nichols. / Thesis (Ph.D.)--The Florida State University, 1988.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_77951 |
| Contributors | Williams, Roselyn Elaine., Florida State University |
| Source Sets | Florida State University |
| Language | English |
| Detected Language | English |
| Type | Text |
| Format | 96 p. |
| Rights | On campus use only. |
| Relation | Dissertation Abstracts International |
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