HOM-ANTICENTER SYMMETRIC ALGEBRAS AND HOM-MOCK LIE ALGEBRAS: MATCHED PAIRS AND MANIN TRIPLES

This work develops the hom-algebra theory for anticenter-symmetric algebras by introducing the concept of a hom-anticenter-symmetric algebra. We give their bimodules, dual bimodules and matched pairs. The relation of the bimodules and matched pairs of hom-anticenter-symmetric algebras between those of hom-Mock Lie algebras is discussed. Finally, we establish the Manin triple of hom-anticenter-symmetric algebras.