A new series of axial algebras of Monster type (2\(\eta\),\(\eta\)) related to the extended symmetric groups

Alsaeedi, Mashaer (2022). A new series of axial algebras of Monster type (2\(\eta\),\(\eta\)) related to the extended symmetric groups. University of Birmingham. Ph.D.

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Abstract

The main aim of this work is to construct several new series of axial algebras of Monster type (2\(\eta\),\(\eta\)). These arise as subalgebras of the Matsuo algebras generated by singles and doubles with respect to a flip, an automorphism of order 2. First, we construct a new series of algebras of dimension \(n^2\) in an ad hoc way, as subalgebras of the Matsuo algebra M\(_\eta\)(\(O^\epsilon_{n+1}\)(3)) and investigate the properties of these new algebras. Towards the end of the thesis, we determine all classes of flips \(\sigma\) for the extended symmetic group 2\(^{n−1}\):S\(_n\). Then, for each class of flips, we construct the fixed subalgebras M\(_\sigma\) and determine their basic combinatorial properties. Furthermore, we identify the values of the parameter \(\eta\), for which these new algebras are not simple and determine the dimension of the radical in
each case.

Type of Work:

Thesis (Doctorates > Ph.D.)

Award Type:

Doctorates > Ph.D.

Supervisor(s):