Extending structures of lie conformal superalgebras

Abstract

In this article, we generalize the $\mathbb{C}[\partial ]$-split extending structures problem of Lie conformal algebras to the super case. First, we introduce a unified product of a given Lie conformal superalgebra $\mathcal{R}$ and a given ${\mathbb{Z}}_2$-graded $\mathbb{C}[\partial ]$-module Q. This product includes some other products such as the twisted product, crossed product, and bicrossed product. Second, using these products, we describe and classify all Lie conformal superalgebra structures on $E=\mathcal{R}\oplus Q$ when $\mathcal{R}$ and Q satisfy some conditions.

Keywords:

• Bicrossed product
• crossed product
• extending structures
• lie conformal superalgebra
• twisted product
• unified product

2010 Mathematics Subject Classification:

• 16S70
• 17A42
• 17B10
• 17B56
• 17B70

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Supported by NNSF of China [Nos. 11771069, 11471090 and 11301109], NSF of Jilin province [No. 20170101048JC] and the project of jilin province department of education [No. JJKH20180005K].