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Nilpotent Lie Algebras

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Nilpotent Ue algebras have played an Important role over the last ye!US : either In the domain at Algebra when one considers Its r... Weiterlesen
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Beschreibung

Nilpotent Ue algebras have played an Important role over the last ye!US : either In the domain at Algebra when one considers Its role In the classlftcation problems of Ue algebras, or In the domain of geometry since one knows the place of nilmanlfolds In the Illustration, the description and representation of specific situations. The first fondamental results In the study of nilpotent Ue algebras are obvlsouly, due to Umlauf. In his thesis (leipZig, 1991), he presented the first non trlvlal classifications. The systematic study of real and complex nilpotent Ue algebras was Independently begun by D1xmler and Morozov. Complete classifications In dimension less than or equal to six were given and the problems regarding superior dimensions brought to light, such as problems related to the existence from seven up, of an infinity of non Isomorphic complex nilpotent Ue algebras. One can also find these losts (for complex and real algebras) In the books about differential geometry by Vranceanu. A more formal approach within the frame of algebraiC geometry was developed by Michele Vergne. The variety of Ue algebraiC laws Is an affine algebraic subset In this view the role variety and the nilpotent laws constitute a Zarlski's closed of Irreduclbl~ components appears naturally as well the determination or estimate of their numbers. Theoritical physiCiSts, Interested In the links between diverse mechanics have developed the Idea of contractions of Ue algebras (Segal, Inonu, Wlgner). That Idea was In fact very convenient In the determination of components.

Inhalt

Preface. 1. Lie Algebras. Generalities. 2. Some Classes of Nilpotent Lie Algebras. 3. Cohomology of Lie Algebras. 4. Cohomology of Some Nilpotent Lie Algebras. 5. The Algebraic Variety of the Laws of Lie Algebras. 6. Variety of Nilpotent Lie Algebras. 7. Characteristically Nilpotent Lie Algebras. 8. Applications to Differential Geometry. The Nilmanifolds. Bibliography. Index.

Produktinformationen

Titel: Nilpotent Lie Algebras
Autor:
EAN: 9780792339328
ISBN: 0792339320
Format: Fester Einband
Herausgeber: Springer Netherlands
Anzahl Seiten: 356
Gewicht: 699g
Größe: H241mm x B160mm x T24mm
Jahr: 1996
Auflage: 1996

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