## Tohoku Mathematical Journal 2015 December SECOND SERIES VOL. 67, NO. 4

 Tohoku Math. J. 67 (2015), 481-493

Title BILINEAR DIFFERENTIAL OPERATORS: PROJECTIVELY EQUIVARIANT SYMBOL AND QUANTIZATION MAPS

Author Taher Bichr, Jamel Boujelben and Khaled Tounsi

(Received March 10, 2014, revised July 3, 2014)
Abstract. We study the space of bilinear differential operators on weighted densities as a module over $\mathrm{sl}(2,{\mathbb R})$. We introduce the corresponding space of symbols and we prove the existence and the uniqueness of canonical projective equivariant symbol and quantization maps.

Mathematics Subject Classification. Primary 53D55.

Key words and phrases. Bilinear differential operators, densities, projective algebra, symbol map.