The 3A-axes are one of four famous families of vectors which in union span the acclaimed Monster algebra. Existing in 4-dimensional subalgebras generated by a pair of 2A-axes, they are idempotents of length 8/5. Inside the Monster algebra, these idempotents have a special association with, and are indexed by the 3A-elements of the Monster. It is therefore paramount to understand these axes in order to further understand the Monster. This thesis sets out to uncover the many properties and profound consequences of the 3A-axes. We present three main accomplishments. The first is an axiomatic approach. Properties of the 3A-axes in the Monster algebra are first proven. These properties are then axiomatized as the definition of what we call a standard 3A-axis. The second is on the (2A,3A)-configurations. This is the study of subalgebras of the Monster algebra generated by a 2A- and 3A-axis. The algebra products between a 2A- and 3A-axis for three new cases are discovered. We also present the structures of several subalgebras generated by a 2A- and 3A-axis for the very first time. The third central result is the successful formulation of a methodology for determining all values of inner products between two 3A-axes contained in a very prominent Majorana algebra. There has been much interest especially in Majorana theory in this algebra associated with A12. The inner product classification achieved in this thesis contributes towards this open topic notably in the study of linear spans of axes.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:726954 |
| Date | January 2017 |
| Creators | Lim, Chien Sheng |
| Contributors | Ivanov, Alexander |
| Publisher | Imperial College London |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://hdl.handle.net/10044/1/52460 |
Page generated in 0.0018 seconds