By Damien Calaque
The Duflo isomorphism first seemed in Lie concept and illustration conception. it really is an isomorphism among invariant polynomials of a Lie algebra and the heart of its common enveloping algebra, generalizing the pioneering paintings of Harish-Chandra on semi-simple Lie algebras. Kontsevich later sophisticated Duflo's lead to the framework of deformation quantization and in addition saw that there's a comparable isomorphism among Dolbeault cohomology of holomorphic polyvector fields on a fancy manifold and its Hochschild cohomology. This ebook, which arose from a sequence of lectures through Damien Calaque at ETH, derives those isomorphisms from a Duflo-type consequence for $Q$-manifolds. All notions pointed out above are brought and defined during this booklet. the single necessities are easy linear algebra and differential geometry. as well as ordinary notions corresponding to Lie (super) algebras, advanced manifolds, Hochschild and Chevalley-Eilenberg cohomologies, spectral sequences, Atiyah and Todd sessions, the graphical calculus brought by way of Kontsevich in his seminal paintings on deformation quantization is addressed intimately. This ebook is definitely fitted to graduate scholars in arithmetic and mathematical physics in addition to researchers operating in Lie idea, algebraic geometry, and deformation idea. A booklet of the eu Mathematical Society (EMS). disbursed in the Americas by means of the yankee Mathematical Society.
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