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Title
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Hochschild cohomology, the characteristic morphism and derived deformations
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Author
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Abstract
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| 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. |
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Language
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English
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Source (journal)
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Compositio mathematica. - Groningen
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Publication
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Groningen
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2008
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ISSN
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0010-437X
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DOI
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10.1112/S0010437X08003655
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Volume/pages
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144
:6
(2008)
, p. 1557-1580
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ISI
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000261869000009
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Full text (Publisher's DOI)
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Full text (open access)
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