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Lectures on Duflo Isomorphisms in Lie Algebra and Complex Geometry

Buch
24,00 € Lieferbar in 2-3 Tagen

Kurzbeschreibung

Duflo isomorphism first appeared in Lie theory and representation theory. It is an isomorphism between invariant polynomials of a Lie algebra and the center of its universal enveloping algebra, generalizing the pioneering work of Harish-Chandra on semi-simple Lie algebras. Later on, Duflo’s result was refound by Kontsevich in the framework of deformation quantization, who also observed that there is a similar isomorphism between Dolbeault cohomology of holomorphic polyvector fields on a complex manifold and its Hochschild cohomology. The present book, which arose from a series of lectures by the first author at ETH, derives these two isomorphisms from a Duflo-type result for Q-manifolds.
All notions mentioned above are introduced and explained in the book, the only prerequisites being basic linear algebra and differential geometry. In addition to standard notions such as Lie (super)algebras, complex manifolds, Hochschild and Chevalley–Eilenberg cohomologies, spectral sequences, Atiyah and Todd classes, the graphical calculus introduced by Kontsevich in his seminal work on deformation quantization is addressed in details.
The book is well-suited for graduate students in mathematics and mathematical physics as well as for researchers working in Lie theory, algebraic geometry and deformation theory.

Details
Schlagworte

Titel: Lectures on Duflo Isomorphisms in Lie Algebra and Complex Geometry
Autoren/Herausgeber: Damien Calaque, Carlo A. Rossi
Aus der Reihe: EMS Series of Lectures in Mathematics
Ausgabe: 1., Aufl.

ISBN/EAN: 9783037190968

Seitenzahl: 106
Format: 24 x 17 cm
Produktform: Taschenbuch/Softcover
Gewicht: 238 g
Sprache: Englisch

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