Comptes Rendus
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

Carlo A. Rossi1
1 MPIM Bonn, Vivatsgasse 7, 53111 Bonn, Germany
Comptes Rendus. Mathématique, Volume 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
Carlo A. Rossi 1

1 MPIM Bonn, Vivatsgasse 7, 53111 Bonn, Germany 
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Carlo A. Rossi. The explicit equivalence between the standard and the logarithmic star product for Lie algebras, II. Comptes Rendus. Mathématique, Volume 350 (2012) no. 15-16, pp. 745-748. doi : 10.1016/j.crma.2012.09.003. https://comptes-rendus.academie-sciences.fr/mathematique/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] Damien Calaque; Giovanni Felder Deformation quantization with generators and relations, J. Algebra, Volume 337 (2011), pp. 1-12 | DOI

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

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

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

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

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

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

[10] Carlo A. Rossi 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] Boris Shoikhet Kontsevich formality and PBW algebras, 2007 | arXiv

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

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

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