Graded Left Symmetric Pseudo-algebras

Abstract

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] 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]. We investigate the left symmetric structure of Lie H-pseudoalgebras W(𝔟), S(𝔟), and He defined in [3].

Key Words:

• Conformal algebra
• Left symmetric algebra
• Pseudoalgebra
• Superalgebra

2010 Mathematics Subject Classification:

• Primary: 16W30
• 17B30
• 17B60
• 17B68
• 17B99
• Secondary: 16S30

ACKNOWLEDGMENT

The author would like to thank the referee for careful reading and many helpful suggestions and comments on this paper.

Notes

Communicated by A. Elduque.