2018/09/19 by Das, Apurba
#16D20 #16E40 #16E45 #17A99 #55U15 #FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.1809.07024
A hom-associative algebra is an algebra whose associativity is twisted by an algebra homomorphism. In this paper, we introduce a strongly homotopy version of hom-associative algebras (HA_∞-algebras in short) on a graded vector space. We describe 2-term HA_∞-algebras in details. In particular, we study 'skeletal' and 'strict' 2-term HA_∞-algebras. We also introduce hom-associative 2-algebras as categorification of hom-associative algebras. The category of 2-term HA_∞-algebras and the category of hom-associative 2-algebras are shown to be equivalent. An appropriate skew-symmetrization of HA_∞-algebras give rise to HL_∞-algebras introduced by Sheng and Chen. Finally, we define a suitable Hochschild cohomology theory for HA_∞-algebras which control the deformation of the structures.