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# ðŸ“™ Lectures on Duflo Isomorphisms in Lie Algebra and Complex Geometry (EMS Series of Lectures in Mathematics) by Damien Calaque, Carlo A. Rossi â€” free pdf

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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.

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- Author:
**Damien Calaque, Carlo A. Rossi** - Year:
**2011** - Publisher:
**European Mathematical Society** - Language:
**English** - ISBN:
**3037190965,9783037190968**

- File size:
**889 939** - Format:
**pdf**

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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 sem...

The representation theory of affine lie algebras has been developed in close connection with various areas of mathematics and mathematical physics in the last two decades. There are three valuable works on it, written by Victor G Kac. This volume begins w...

The study of Fourier transforms of invariant functions on finite reductive Lie algebras has been initiated by T.A. Springer (1976) in connection with the geometry of nilpotent orbits. In this book the author studies Fourier transforms using Deligne-Luszti...

The representation theory of affine lie algebras has been developed in close connection with various areas of mathematics and mathematical physics in the last two decades. There are three valuable works on it, written by Victor G Kac. This volume begins w...

In 1914, E. Cartan posed the problem of finding all irreducible real linear Lie algebras. Iwahori gave an updated exposition of Cartan's work in 1959. This theory reduces the classification of irreducible real representations of a real Lie algebra to a de...

The representation theory of affine lie algebras has been developed in close connection with various areas of mathematics and mathematical physics in the last two decades. There are three valuable works on it, written by Victor G Kac. This volume begins w...

This book offers a wide-ranging introduction to algebraic geometry along classical lines. It consists of lectures on topics in classical algebraic geometry, including the basic properties of projective algebraic varieties, linear systems of hypersurfaces,...

This book offers a wide-ranging introduction to algebraic geometry along classical lines. It consists of lectures on topics in classical algebraic geometry, including the basic properties of projective algebraic varieties, linear systems of hypersurfaces,...

This book describes a new and original formalism based on mirror symmetries of Lie groups, Lie algebras and Homogeneous spaces. Special systems of mirrors are used for classification purposes and as an instrument for studies of Homogeneous spaces. Tri-sym...