no. 15-16
Lie Algebras/Mathematical Physics
The explicit equivalence between the standard and the logarithmic star product for Lie algebras, II
[Une équivalence explicite entre les produit-étoilés standard et logarithmique pour une algèbre de Lie, II]

Présenté par : Michèle Vergne

Rossi, Carlo A.1
1 MPIM Bonn, Vivatsgasse 7, 53111 Bonn, Germany
Comptes Rendus. Mathématique, Tome 350 (2012) no. 15-16, pp. 745-748.

On donne la démonstration détaillée de Rossi (2012) [10, Théorème 3.3] ; après, on commente la nature de ce résultat and sa relation avec le groupe de Grothendieck–Teichmüller.

We give a detailed proof of Rossi (2012) [10, Theorem 3.3] and comment on its nature and its relationship with the Grothendieck–Teichmüller group.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2012.09.003
Rossi, Carlo A. 1

1 MPIM Bonn, Vivatsgasse 7, 53111 Bonn, Germany 
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Rossi, Carlo A. The explicit equivalence between the standard and the logarithmic star product for Lie algebras, II. Comptes Rendus. Mathématique, Tome 350 (2012) no. 15-16, pp. 745-748. doi : 10.1016/j.crma.2012.09.003. http://www.numdam.org/articles/10.1016/j.crma.2012.09.003/

[1] Anton Alekseev, Johannes Löffler, Carlo A. Rossi, Charles Torossian, Stokesʼ Theorem in presence of poles and logarithmic singularities, 2012, in preparation.

[2] Anton Alekseev, Johannes Löffler, Carlo A. Rossi, Charles Torossian, The logarithmic formality quasi-isomorphism, 2012, in preparation.

[3] Calaque, Damien; Felder, Giovanni Deformation quantization with generators and relations, J. Algebra, Volume 337 (2011), pp. 1-12 | DOI

[4] Calaque, Damien; Felder, Giovanni; Ferrario, Andrea; Rossi, Carlo A. Bimodules and branes in deformation quantization, Compos. Math., Volume 147 (2011) no. 1, pp. 105-160 | DOI

[5] Cattaneo, Alberto S.; Felder, Giovanni Relative formality theorem and quantisation of coisotropic submanifolds, Adv. Math., Volume 208 (2007) no. 2, pp. 521-548 | DOI

[6] Cattaneo, Alberto S.; Rossi, Carlo A.; Torossian, Charles Biquantization of symmetric pairs and the quantum shift, 2011 | arXiv

[7] Kontsevich, Maxim Operads and motives in deformation quantization, Moshé Flato (1937–1998), Lett. Math. Phys., Volume 48 (1999) no. 1, pp. 35-72 | DOI

[8] Kontsevich, Maxim Deformation quantization of Poisson manifolds, Lett. Math. Phys., Volume 66 (2003) no. 3, pp. 157-216

[9] Merkulov, Sergei Exotic automorphisms of the Schouten algebra of polyvector fields, 2008 | arXiv

[10] Rossi, Carlo A. The explicit equivalence between the standard and the logarithmic star product for Lie algebras, I, C. R. Acad. Sci. Paris, Ser. I, Volume 350 (2012) no. 13–14, pp. 661-664 | DOI

[11] Shoikhet, Boris Kontsevich formality and PBW algebras, 2007 | arXiv

[12] Willwacher, Thomas A counterexample to the quantizability of modules, Lett. Math. Phys., Volume 81 (2007) no. 3, pp. 265-280

[13] Willwacher, Thomas M. Kontsevichʼs graph complex and the Grothendieck–Teichmüller Lie algebra, 2010 | arXiv

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