Maximal Nilpotent Subalgebras II: A Correspondence Theorem Within Solvable Associative Algebras. With 242 Exercises
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| Title: | Maximal Nilpotent Subalgebras II: A Correspondence Theorem Within Solvable Associative Algebras. With 242 Exercises |
|---|---|
| Description: | Within series II we extend the theory of maximal nilpotent substructures to solvable associative algebras, especially for their group of units and their associated Lie algebra. We construct all maximal nilpotent Lie subalgebras and characterize them by simple and double centralizer properties. They possess distinctive attractor and repeller characteristics. Their number of isomorphic classes is finite and can be bounded by Bell numbers. Cartan subalgebras and the Lie nilradical are extremal among all maximal nilpotent Lie subalgebras. The maximal nilpotent Lie subalgebras are connected to the maximal nilpotent subgroups. This correspondence is bijective via forming the group of units and creating the linear span. Cartan subalgebras and Carter subgroups as well as the Lie nilradical and the Fitting subgroup are linked by this correspondence. All partners possess the same class of nilpotency based on a theorem of Xiankun Du. By using this correspondence we transfer all results to maximal nilpotent subgroups of the group of units. Carter subgroups and the Fitting subgroup turn out to be extremal among all maximal nilpotent subgroups. All four extremal substructures are proven to be Fischer subgroups, Fischer subalgebras, nilpotent injectors and projectors. 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. |
| Authors: | Wirsing, Sven Bodo |
| Resource Type: | eBook. |
| Subjects: | Associative algebras |
| Categories: | MATHEMATICS / Algebra / Intermediate |
| Database: | eBook Collection (EBSCOhost) |
| FullText | Links: – Type: ebook-pdf Text: Availability: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Maximal Nilpotent Subalgebras II: A Correspondence Theorem Within Solvable Associative Algebras. With 242 Exercises – Name: Abstract Label: Description Group: Ab Data: Within series II we extend the theory of maximal nilpotent substructures to solvable associative algebras, especially for their group of units and their associated Lie algebra. We construct all maximal nilpotent Lie subalgebras and characterize them by simple and double centralizer properties. They possess distinctive attractor and repeller characteristics. Their number of isomorphic classes is finite and can be bounded by Bell numbers. Cartan subalgebras and the Lie nilradical are extremal among all maximal nilpotent Lie subalgebras. The maximal nilpotent Lie subalgebras are connected to the maximal nilpotent subgroups. This correspondence is bijective via forming the group of units and creating the linear span. Cartan subalgebras and Carter subgroups as well as the Lie nilradical and the Fitting subgroup are linked by this correspondence. All partners possess the same class of nilpotency based on a theorem of Xiankun Du. By using this correspondence we transfer all results to maximal nilpotent subgroups of the group of units. Carter subgroups and the Fitting subgroup turn out to be extremal among all maximal nilpotent subgroups. All four extremal substructures are proven to be Fischer subgroups, Fischer subalgebras, nilpotent injectors and projectors. 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. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Wirsing%2C+Sven+Bodo%22">Wirsing, Sven Bodo</searchLink> – Name: TypePub Label: Resource Type Group: TypPub Data: eBook. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Associative+algebras%22">Associative algebras</searchLink> – Name: SubjectBISAC Label: Categories Group: Su Data: <searchLink fieldCode="ZK" term="%22MATHEMATICS+%2F+Algebra+%2F+Intermediate%22">MATHEMATICS / Algebra / Intermediate</searchLink> |
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| RecordInfo | BibRecord: BibEntity: Classifications: – Code: 512.4 Scheme: ddc Type: prePub Languages: – Code: eng Text: English Subjects: – SubjectFull: Associative algebras Type: general Titles: – TitleFull: Maximal Nilpotent Subalgebras II: A Correspondence Theorem Within Solvable Associative Algebras. With 242 Exercises Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Wirsing, Sven Bodo – PersonEntity: Name: NameFull: Wirsing, Sven Bodo IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Type: published Y: 2018 – D: 02 M: 04 Type: profile Y: 2019 Identifiers: – Type: isbn-print Value: 9783960671961 – Type: isbn-electronic Value: 9783960676966 Numbering: – Type: volume Value: II Titles: – TitleFull: Maximal Nilpotent Subalgebras II: A Correspondence Theorem Within Solvable Associative Algebras. With 242 Exercises Type: main |
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