02716nam a22003735a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084002900185100003000214245012800244260008200372300003400454336002600488337002600514338003600540347002400576490006100600506006600661520134800727650002702075650004002102650002802142650004302170700003002213856003202243856006702275128-110524CH-001817-320110524234510.0a fot ||| 0|cr nn mmmmamaa110524e20110611sz fot ||| 0|eng d a978303719596370a10.4171/0962doi ach0018173 7aPBFL2bicssc a13-xxa14-xxa17-xx2msc1 aCalaque, Damien,eauthor.10aLectures on Duflo Isomorphisms in Lie Algebra and Complex Geometryh[electronic resource] /cDamien Calaque, Carlo A. Rossi3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2011 a1 online resource (114 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Lectures in Mathematics (ELM) ;x2523-51761 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aDuflo 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.07aFields & rings2bicssc07aCommutative rings and algebras2msc07aAlgebraic geometry2msc07aNonassociative rings and algebras2msc1 aRossi, Carlo A.,eauthor.40uhttps://doi.org/10.4171/096423cover imageuhttps://www.ems-ph.org/img/books/calaque_mini.jpg