Graded Left Symmetric Pseudo-algebras

In the present article, we introduce G-graded left symmetric H-pseudoalgebras, where G is a grading group, and H is a cocommutative Hopf algebra. Some results about associative H-pseudoalgebras in 23 Retakh , A. ( 2004 ). Unital associative pseudoalgebras and their representations . J. Algebra 227 : 769 – 805 .Crossref] , Google Scholar]] are generalized. The commutator algebras of the G-graded left symmetric H-pseudo-algebras are Lie H-pseudoalgebras, which are classified when the grading group is trivial in 3 Bakalov , B. , D'Andrea , A. , Kac , V. G. ( 2001 ). Theory of finite pseudoalgebras . Adv. in Math. 162 : 1 – 140 .Crossref], Web of Science ®] , Google Scholar]]. We investigate the left symmetric structure of Lie H-pseudoalgebras W(𝔟), S(𝔟), and He defined in 3 Bakalov , B. , D'Andrea , A. , Kac , V. G. ( 2001 ). Theory of finite pseudoalgebras . Adv. in Math. 162 : 1 – 140 .Crossref], Web of Science ®] , Google Scholar]].