[arXiv:1209.1261] Involutive A-infinity algebras and dihedral cohomology from arXiv Front: math.KT by Christopher Braun Notions of homotopy involutive associative algebras and homotopy cyclic involutive associative algebras, which will be called involutive A-infinity algebras and cyclic involutive A-infinity algebras, are defined and studied in some detail and the cohomology theories associated to such structures are identified and related to dihedral cohomology. The deformation theory associated to these algebras is also examined. Generalisations to involutive algebras over arbitrary Koszul operads are briefly considered.
nLab page on Dihedral cohomology