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

Textbook 2016 241 Pages

Mathematics - Algebra

Summary

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.

Details

Pages
241
Type of Edition
Erstausgabe
Year
2016
ISBN (eBook)
9783960676034
ISBN (Book)
9783960671039
File size
10.6 MB
Language
English
Catalog Number
v349138
Grade
Tags
Cartan subalgebra Nilradical Lie algebra Associative algebra Maximal nilpotent Group algebra Exercise Lie nilpotency Salvatore Siciliano

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