For an associative algebra A, we consider the pair "the Hochschild cochain complex C•(A,A) and the algebra A". There is a natural 2-colored operad which acts on this pair. We show that this operad is quasi-isomorphic to the singular chain operad of Voronov's Swiss Cheese operad. This statement is the Swiss Cheese version of the Deligne conjecture formulated by M. Kontsevich ["Operads and motives in deformation quantization." Letters in Mathematical Physics 48 (1999) 35-72.].
ASJC Scopus subject areas