TY - JOUR
T1 - Deformations of algebroid stacks
AU - Bressler, Paul
AU - Gorokhovsky, Alexander
AU - Nest, Ryszard
AU - Tsygan, Boris
N1 - Funding Information:
* Corresponding author. E-mail addresses: [email protected] (P. Bressler), [email protected] (A. Gorokhovsky), [email protected] (R. Nest), [email protected] (B. Tsygan). 1 Partially supported by NSF grants DMS-0400342 and DMS-0900968. 2 Partially supported by NSF grants DMS-0605030 and DMS-0906391.
PY - 2011/3/1
Y1 - 2011/3/1
N2 - In this paper we consider deformations of an algebroid stack on an étale groupoid. We construct a differential graded Lie algebra (DGLA) which controls this deformation theory. In the case when the algebroid is a twisted form of functions we show that this DGLA is quasiisomorphic to the twist of the DGLA of Hochschild cochains on the algebra of functions on the groupoid by the characteristic class of the corresponding gerbe.
AB - In this paper we consider deformations of an algebroid stack on an étale groupoid. We construct a differential graded Lie algebra (DGLA) which controls this deformation theory. In the case when the algebroid is a twisted form of functions we show that this DGLA is quasiisomorphic to the twist of the DGLA of Hochschild cochains on the algebra of functions on the groupoid by the characteristic class of the corresponding gerbe.
KW - Algebroid stacks
KW - Deformation quantization
KW - Gerbes
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U2 - 10.1016/j.aim.2010.10.008
DO - 10.1016/j.aim.2010.10.008
M3 - Article
AN - SCOPUS:78651518689
SN - 0001-8708
VL - 226
SP - 3018
EP - 3087
JO - Advances in Mathematics
JF - Advances in Mathematics
IS - 4
ER -