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Lectures on Duflo Isomorphisms in Lie Algebra and Complex Geometry
 
Damien Calaque ETH, Zurich, Switzerland
Carlo A. Rossi Max Planck Institute for Mathematics, Bonn, Germany
A publication of European Mathematical Society
Lectures on Duflo Isomorphisms in Lie Algebra and Complex Geometry
Softcover ISBN:  978-3-03719-096-8
Product Code:  EMSSERLEC/14
List Price: $32.00
AMS Member Price: $25.60
Please note AMS points can not be used for this product
Lectures on Duflo Isomorphisms in Lie Algebra and Complex Geometry
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Lectures on Duflo Isomorphisms in Lie Algebra and Complex Geometry
Damien Calaque ETH, Zurich, Switzerland
Carlo A. Rossi Max Planck Institute for Mathematics, Bonn, Germany
A publication of European Mathematical Society
Softcover ISBN:  978-3-03719-096-8
Product Code:  EMSSERLEC/14
List Price: $32.00
AMS Member Price: $25.60
Please note AMS points can not be used for this product
  • Book Details
     
     
    EMS Series of Lectures in Mathematics
    Volume: 142011; 114 pp
    MSC: Primary 13; 17; 14

    The 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. Kontsevich later refined Duflo's result in the framework of deformation quantization and also observed that there is a similar isomorphism between Dolbeault cohomology of holomorphic polyvector fields on a complex manifold and its Hochschild cohomology. This book, which arose from a series of lectures by Damien Calaque at ETH, derives these two isomorphisms from a Duflo-type result for \(Q\)-manifolds.

    All notions mentioned above are introduced and explained in this book. The only prerequisites are 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 detail.

    This book is well suited for graduate students in mathematics and mathematical physics as well as researchers working in Lie theory, algebraic geometry, and deformation theory.

    A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.

    Readership

    Graduate students and research mathematicians interested in algebra.

  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 142011; 114 pp
MSC: Primary 13; 17; 14

The 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. Kontsevich later refined Duflo's result in the framework of deformation quantization and also observed that there is a similar isomorphism between Dolbeault cohomology of holomorphic polyvector fields on a complex manifold and its Hochschild cohomology. This book, which arose from a series of lectures by Damien Calaque at ETH, derives these two isomorphisms from a Duflo-type result for \(Q\)-manifolds.

All notions mentioned above are introduced and explained in this book. The only prerequisites are 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 detail.

This book is well suited for graduate students in mathematics and mathematical physics as well as researchers working in Lie theory, algebraic geometry, and deformation theory.

A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.

Readership

Graduate students and research mathematicians interested in algebra.

Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.