The recognition theorem for graded Lie algebras in prime characteristic / / Georgia Benkart, Thomas Gregory, Alexander Premet

• Record Nr.: UNINA9910827764803321
• Autore: Benkart Georgia <1949->
• Pubbl/distr/stampa: Providence, Rhode Island : , : American Mathematical Society, , 2009; ©2009
• ISBN: 1-4704-0526-1
• Descrizione fisica: 1 online resource (164 p.)
• Collana: Memoirs of the American Mathematical Society, , 0065-9266 ; ; Volume 197, Number 920
• Disciplina: 512/.482
• Soggetti: Lie algebras
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: "Volume 197, Number 920 (second of 5 numbers)."
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: ""Contents""; ""Introduction""; ""Chapter 1. Graded Lie Algebras""; ""1.1. Introduction""; ""1.2. The Weisfeiler radical""; ""1.3. The minimal ideal J""; ""1.4. The graded algebras B(V[sub(-t)]) and B(V[sub(t)])""; ""1.5. The local subalgebra""; ""1.6. General properties of graded Lie algebras""; ""1.7. Restricted Lie algebras""; ""1.8. The main theorem on restrictedness (Theorem 1.63)""; ""1.9. Remarks on restrictedness""; ""1.10. The action of g[sub(0)] on g[sub(-j)]""; ""1.11. The depth-one case of Theorem 1.63""; ""1.12. Proof of Theorem 1.63 in the depth-one case""; ""2.7. Divided power algebras""""2.8. Witt Lie algebras of Cartan type (the W series)""; ""2.9. Special Lie algebras of Cartan type (the S series)""; ""2.10. Hamiltonian Lie algebras of Cartan type (the H series)""; ""2.11. Contact Lie algebras of Cartan type (the K series)""; ""2.12. The Recognition Theorem with stronger hypotheses""; ""2.13. g[sub(l)] as a g[sub(0)]-module for Lie algebras g of Cartan type""; ""2.14. Melikyan Lie algebras""; ""Chapter 3. The Contragredient Case""; ""3.1. Introduction""; ""3.2. Results on modules for three-dimensional Lie algebras""; ""3.3. Primitive vectors in g[sub(1)] and g[sub(-1)]""""3.4. Subalgebras with a balanced grading""; ""3.5. Algebras with an unbalanced grading""; ""Chapter 4. The Noncontragredient Case""; ""4.1. General assumptions and notation""; ""4.2. Brackets of weight vectors in ; opposite gradation spaces""; ""4.3. Determining g[sub(0)] and its representation on g[sub(-1)]""; ""4.4. Additional assumptions""; ""4.5. Computing weights of b[sup(â€?)]-primitive vectors in g[sub(1)]""; ""4.6. Determination of the local Lie algebra""; ""4.7. The irreducibility of g[sub(1)]""; ""4.8. Determining the negative part when g[sub(1)] is irreducible""""4.9. Determining the negative part when g[sub(1)] is reducible""; ""4.10. The case that g[sub(0)] is abelian""; ""4.11. Completion of the proof of the Main Theorem""; ""Bibliography""