The first cohomology of W(2) with coefficients in Kac modules

Abstract

Over a field of characteristic $p>2,$ the first cohomology of the Witt-type Lie superalgebra W(2) with coefficients in all Kac modules $K(\lambda )$ is determined by use of the weight-derivation spaces from W(2) to $K(\lambda )$.

KEYWORDS:

• Kac modules
• the first cohomology
• W(2)

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 17B50
• 17B40

Additional information

Funding

Supported by the NSF of Heilongjiang Province (YQ2020A005) and the NSF of China (12061029).