Bibliography: leaves 54-55.

Thesis (M. Sc.)--University of Adelaide, 1988. / Includes bibliographical references (leaves 54-55).

Thesis (Ph. D.)--Hong Kong University of Science and Technology, 2004. / Includes bibliographical references (leaves 51-52). Also available in electronic version. Access restricted to campus users.

Clifford algebras have been studied for many years and their algebraic properties are well known. In particular, all Clifford algebras have been classified as matrix algebras over one of the three division algebras. But Clifford Algebras are far more interesting than this classification suggests; they provide the algebraic basis for a unified language for physics and mathematics which offers many advantages over current techniques. This language is called geometric algebra - the name originally chosen by Clifford for his algebra - and this thesis is an investigation into the properties and applications of Clifford's geometric algebra. The work falls into three broad categories: - The formal development of geometric algebra has been patchy and a number of important subjects have not yet been treated within its framework. A principle feature of this thesis is the development of a number of new algebraic techniques which serve to broaden the field of applicability of geometric algebra. Of particular interest are an extension of the geometric algebra of spacetime (the spacetime algebra) to incorporate multiparticle quantum states, and the development of a multivector calculus for handling differentiation with respect to a linear function. - A central contention of this thesis is that geometric algebra provides the natural language in which to formulate a wide range of subjects from modern mathematical physics. To support this contention, reformulations of Grassmann calculus, Lie algebra theory, spinor algebra and Lagrangian field theory are developed. In each case it is argued that the geometric algebra formulation is computationally more efficient than standard approaches, and that it provides many novel insights. - The ultimate goal of a reformulation is to point the way to new mathematics and physics, and three promising directions are developed. The first is a new approach to relativistic multiparticle quantum mechanics. The second deals with classical models for quantum spin-I/2. The third details an approach to gravity based on gauge fields acting in a fiat spacetime. The Dirac equation forms the basis of this gauge theory, and the resultant theory is shown to differ from general relativity in a number of its features and predictions.

Thesis (Ph. D.)--University of Oregon, 2007. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 130-131). Also available for download via the World Wide Web; free to University of Oregon users.

No description available.

Graduation date: 1994

With the classification of finite simple groups having been completed in 1981, recent work in group theory has involved the study of the structures of simple groups. The character tables of maximal subgroups of simple groups give substantive information about these groups. Most of the maximal subgroups of simple groups are of extension type. Some of the maximal subgroups of simple groups contain constituents of the generalized symmetric groups. Here we shall be interested in discussing such groups which we may call groups associated with the generalized symmetric groups. There are several well developed methods for calculating the character tables of group extensions. However Fischer [17] has given an effective method for calculating the character tables of some group extensions including the generalized symmetric group B (m, n). Actually work on the characters of wreath products with permutation groups dates back to Specht's work [61], through the works of Osima [49] and Kerber [33]. And more recently other people have worked on characters of wreath products with symmetric groups, these amongst others include Darafshesh and Iranmanesh [14], List and Mahmoud [36], Puttaswamiah [52], Read [55, 56], Saeed-Ul-Islam [59] and Stembridge [64]. It is well known that the character table of the generalized symmetric group B(m, n), where m and n are positive integers, can be constructed in GAP [22] with B(m, n) considered as the wreath product of the cyclic group Zm of order m with the symmetric group Sn' For example Pfeiffer [50] has given programmes which compute the character tables of wreath products with symmetric groups in GAP. However it may be necessary to obtain the partial character table of a group in hand rather than its complete character table. Further due to limited workspace in GAP, the wreath product method can only be used to compute character tables of B(m, n) for small values of m and n. It is for these reasons amongst others that Fischer's method is sometimes used to construct the character tables of such groups. groups B(2, 6) and B(3, 5) of orders 46080 and 29160 is done here. We have also used Programme 5.2.4 to construct the Fischer-Clifford matrices of the groups B(2, 12) and B(4, 5) of orders 222 x 35 X 52 X 7 x 11 and 213 x 3 x 5 respectively. Due to lack of space here we have given the Fischer-Clifford matrices of B(2, 12) and B(4,5) on the compact disk submitted with this thesis. However note that these matrices are the equivalent form of the Fischer-Clifford matrices of B(2, 12) and B(4,5). In [35] R.J. List has presented a method for constructing the Fischer-Clifford matrices of group extensions of an irreducible constituent of the elementary abelian group 2n by a symmetric group. The other aim of our work is to adapt the combinatorial method in [5] to the construction of the Fischer-Clifford matrices of some group extensions associated with B(m, n), using a similar method as the one used in [35]. Examples are given on the application of this adaptation to some groups associated with the groups B(2, 6), B(3,3) and B(3, 5). In this thesis we have constructed the character tables of the groups B(2, 6) and B(3,5) and some group extensions associated with these two groups and B(3, 3). We have also constructed the character tables of the groups B(2, 12) and B(4, 5) in our work, these character tables are given on the compact disk submitted with this thesis. The correctness of all the character tables constructed in this thesis has been tested in GAP. The main working programmes (Programme 2.2.3, Programme 3.1.9, Programme 3.1.10, Programme 5.2.1, Programme 5.2.4 and Programme 5.2.2) are given on the compact disk submitted with this thesis. It is anticipated that with further improvements, a number of the programmes given here will be incorporated into GAP. Indeed with further research work the programmes given here should lead to an alternative programme for computing the character table of B(m, n). / Thesis (Ph.D.)- University of KwaZulu-Natal, Pietermaritzburg, 2005.

Thesis (Ph. D.)--University of Canterbury, 2009. / Typescript (photocopy). "January 2009." Includes bibliographical references (leaves 125-131). Also available via the World Wide Web.

Thesis (M. Sc.)--University of Alberta, 2009. / In the title, the character [k] is in subscript and the character [n] is in superscript. Title from PDF file main screen (viewed on Oct. 19, 2009). "A thesis submitted to the Faculty of Graduate Studies and Research in partial fulfillment of the requirements for the degree of Master of Science in Pure Mathematics, Department of Mathematical and Statistical Sciences, University of Alberta." Includes bibliographical references.