(Co)homology and crossed module for BiHom-associative algebras

BiHom-associative algebras are generalized associative algebras with two multiplicative linear maps. In this paper, we give the Hochschild homology and cyclic homology structure of BiHom-associative algebras. Then, generalize the dual bimodule action to define the cyclic cohomology. Finally, we introduce the crossed modules of BiHom-associative algebras and show that the Hochschild cohomology of BiHomassociative algebra classifies crossed modules. (c) 2024 Elsevier Inc. All rights reserved.