Involutive A-infinity algebras and dihedral cohomology

Braun, Christopher (2014) Involutive A-infinity algebras and dihedral cohomology. Journal of Homotopy and Related Structures, 9 (2). pp. 317-337. ISSN 2193-8407

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Abstract

We define and study the cohomology theories associated to A-infinity algebras and cyclic A-infinity algebras equipped with an involution, generalising dihedral cohomology to the A-infinity context. Such algebras arise, for example, as unoriented versions of topological conformal field theories. It is well known that Hochschild cohomology and cyclic cohomology govern, in a precise sense, the deformation theory of A-infinity algebras and cyclic A-infinity algebras and we give analogous results for the deformation theory in the presence of an involution. We also briefly discuss generalisations of these constructions and results to homotopy algebras over Koszul operads, such as L-infinity algebras or C-infinity algebras equipped with an involution.

Item Type:
Journal Article
Journal or Publication Title:
Journal of Homotopy and Related Structures
Additional Information:
Date of Acceptance: 05/04/2013 The final publication is available at Springer via http://dx.doi.org/10.1007/s40062-013-0030-y
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600/2608
Subjects:
ID Code:
75584
Deposited By:
Deposited On:
11 Sep 2015 12:24
Refereed?:
Yes
Published?:
Published
Last Modified:
09 Jul 2020 03:56