Maximal nilpotent subalgebras I: Nilradicals and Cartan subalgebras in associative algebras. With 428 exercises

Download or read book Maximal nilpotent subalgebras I: Nilradicals and Cartan subalgebras in associative algebras. With 428 exercises written by Sven Bodo Wirsing and published by diplom.de. This book was released on 2016-12-08 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the author’s doctorate time at the Christian-Albrechts-Universitat to Kiel, Salvatore Siciliano gave a stimulating talk in the upper seminar algebra theory about Cartan subalgebras in Lie algebra associates to associative algebra. This talk was the incentive for the author to analyze maximal nilpotent substructures of the Lie algebra associated to associative algebras. In the present work Siciliano's theory about Cartan subalgebras is worked off and expanded to different special associative algebra classes. In addition, a second maximal nilpotent substructure is analyzed: the nilradical. Within this analysis the main focus is to describe these substructure with the associative structure of the underlying algebra. This is successfully realized in this work. Numerous examples (like group algebras and Solomon (Tits-) algebras) illustrate the results to the reader. Within the numerous exercises these results can be applied by the reader to get a deeper insight in this theory.