Publication
Title
Hochschild cohomology, the characteristic morphism and derived deformations
Author
Abstract
 A notion of Hochschild cohomology HH*() of an abelian category was defined by Lowen and Van den Bergh (Adv. Math. 198 (2005), 172221). They also showed the existence of a characteristic morphism ÷ from the Hochschild cohomology of into the graded centre ℨ*(Db()) of the bounded derived category of . An element cHH2() corresponds to a first-order deformation c of (Lowen and Van den Bergh, Trans. Amer. Math. Soc. 358 (2006), 54415483). The problem of deforming an object MDb() to Db(c) was treated by Lowen (Comm. Algebra 33 (2005), 31953223). In this paper we show that the element ÷(c)MExt2(M,M) is precisely the obstruction to deforming M to Db(c). Hence, this paper provides a missing link between the above works. Finally we discuss some implications of these facts in the direction of a derived deformation theory.
Language
English
Source (journal)
Compositio mathematica. - Groningen
Publication
Groningen : 2008
ISSN
0010-437X
Volume/pages
144:6(2008), p. 1557-1580
ISI
000261869000009
Full text (Publisher's DOI)
Full text (open access)
UAntwerpen
 Faculty/Department Research group Publication type Subject Affiliation Publications with a UAntwerp address