On the structure of the Solomon-Tits algebra of the symmetric group. An analysis of associative, group theoretic and Lie theoretical phenomenons

Zusatztext

Within this work we study the structure of the Solomon-Tits algebra of the symmetric group motivated by results of research done by Manfred Schocker about the module structure of this algebra. We investigate three structures: the associative, the associated Lie algebra and the group of units. All three structures are related and can be studied in the more general context of associative soluble splittable algebras possessing a self-centralizing radical complement. Our results are related to dimension formulas, Duo algebras, self-centralization of the radical complements, Cartan subalgebras, Sylow subgroups, Hall subgroups, Carter subgroups, stagnation of central chains, classes of nilpotency and solvability, exponents alongside central chains, nilradical and Fitting subgroup, semisimple and simple substructures, anti-automoprhism and irreducible character values.

Autorenportrait

Sven Bodo Wirsing was born in 1975 in Neumünster. After graduating from high school at KKS in Itzehoe (with a focus on mathematics and physics), he studied mathematics with a minor in business administration (especially logistics) at CAU university in Kiel. He did his doctorate in 2005 on group and algebra theory. During his years of study in Kiel he gained experience in the analysis of interdisciplinary processes, which are reflected in different disciplines of algebra, such as group theory, representation theory, theory of Lie and associative algebras. From this experience, he also studied and analyzed the subject matter of the present work. Since the end of his doctorate, Dr. Wirsing has been working as a senior IT consultant for logistics processes at several renowned companies where he is responsible for logistics optimization and maintenance. Since 2012 he has published several books on algebras.

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