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Maximal Abelian Sets of Roots.
In this work the author lets \Phi be an irreducible root system, with Coxeter group W. He considers subsets of \Phi which are abelian, meaning that no two roots in the set have sum in \Phi \cup \{ 0 \}. He classifies all maximal abelian sets (i.e., abelian sets properly contained in no other) up to...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence :
American Mathematical Society,
2018.
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| Colección: | Memoirs of the American Mathematical Society.
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 001 | EBOOKCENTRAL_on1024275439 | ||
| 003 | OCoLC | ||
| 005 | 20240329122006.0 | ||
| 006 | m o d | ||
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| 020 | |a 9781470442088 | ||
| 020 | |a 1470442086 | ||
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| 035 | |a (OCoLC)1024275439 | ||
| 050 | 4 | |a QA252.3 |b .L398 2018eb | |
| 082 | 0 | 4 | |a 512.482 |2 23 |
| 049 | |a UAMI | ||
| 100 | 1 | |a Lawther, R. | |
| 245 | 1 | 0 | |a Maximal Abelian Sets of Roots. |
| 260 | |a Providence : |b American Mathematical Society, |c 2018. | ||
| 300 | |a 1 online resource (234 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Memoirs of the American Mathematical Society ; |v v. 250 | |
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a Cover; Title page; Chapter 1. Introduction; 1.1. Background and motivation; 1.2. Preliminary results; Chapter 2. Root systems of classical type; 2.1. Root systems of type _{ }; 2.2. Root systems of type _{ }; 2.3. Root systems of type _{ }; 2.4. Root systems of type _{ }; Chapter 3. The strategy for root systems of exceptional type; 3.1. Radical and near-radical sets; 3.2. Proving completeness; 3.3. Identifying stabilizers and structure; Chapter 4. The root system of type â#x82;#x82;; 4.1. Radical maximal abelian sets; 4.2. Determination of maximal abelian sets. | |
| 505 | 8 | |a 4.3. Stabilizers and structure of maximal abelian setsChapter 5. The root system of type â#x82;#x84;; 5.1. Radical maximal abelian sets; 5.2. Determination of maximal abelian sets; 5.3. Stabilizers and structure of maximal abelian sets; Chapter 6. The root system of type â#x82;#x86;; 6.1. Radical maximal abelian sets; 6.2. Determination of maximal abelian sets; 6.3. Stabilizers and structure of maximal abelian sets; Chapter 7. The root system of type â#x82;#x87;; 7.1. Radical maximal abelian sets; 7.2. Near-radical maximal abelian sets; 7.3. Determination of maximal abelian sets. | |
| 505 | 8 | |a 7.4. Stabilizers and structure of maximal abelian setsChapter 8. The root system of type â#x82;#x88;; 8.1. Radical maximal abelian sets; 8.2. Near-radical maximal abelian sets; 8.3. Determination of maximal abelian sets; 8.4. Stabilizers and structure of maximal abelian sets; Chapter 9. Tables of maximal abelian sets; Appendix A. Root trees for root systems of exceptional type; Bibliography; Back Cover. | |
| 520 | |a In this work the author lets \Phi be an irreducible root system, with Coxeter group W. He considers subsets of \Phi which are abelian, meaning that no two roots in the set have sum in \Phi \cup \{ 0 \}. He classifies all maximal abelian sets (i.e., abelian sets properly contained in no other) up to the action of W: for each W-orbit of maximal abelian sets we provide an explicit representative X, identify the (setwise) stabilizer W_X of X in W, and decompose X into W_X-orbits. Abelian sets of roots are closely related to abelian unipotent subgroups of simple algebraic groups, and thus to abelia. | ||
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Root systems (Algebra) | |
| 650 | 0 | |a Lie algebras. | |
| 650 | 0 | |a Abelian groups. | |
| 650 | 6 | |a Systèmes de racines (Algèbre) | |
| 650 | 6 | |a Algèbres de Lie. | |
| 650 | 6 | |a Groupes abéliens. | |
| 650 | 7 | |a Abelian groups |2 fast | |
| 650 | 7 | |a Lie algebras |2 fast | |
| 650 | 7 | |a Root systems (Algebra) |2 fast | |
| 758 | |i has work: |a Maximal abelian sets of roots (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGkTKjxmXb8YGy7HjttTxP |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Lawther, R. |t Maximal Abelian Sets of Roots. |d Providence : American Mathematical Society, ©2018 |z 9781470426798 |
| 830 | 0 | |a Memoirs of the American Mathematical Society. | |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=5291692 |z Texto completo |
| 938 | |a EBL - Ebook Library |b EBLB |n EBL5291692 | ||
| 994 | |a 92 |b IZTAP | ||