2-Cocycles of the Lie Superalgebras of Weyl Type

ABSTRACT

In an article by Su and Zhao, the Lie algebra 𝒜[𝒟] = 𝒜⊗ 𝔽[𝒟] of Weyl type was defined and studied, where 𝒜 is a commutative associative algebra with an identity element over a field 𝔽 of arbitrary characteristic, and 𝔽[𝒟] is the polynomial algebra of a commutative derivation subalgebra 𝒟 of 𝒜. The 2-cocycles of a class of 𝒜[𝒟] were determined by Su. In the present article, we determine the 2-cocycles of a class of Lie superalgebras of Weyl type over a field 𝔽 of characteristic zero.

Keywords:

• 2-cocycle
• Lie superalgebra of Weyl type

Mathematics Subject Classification:

• 17B05
• 17B56
• 17B70

ACKNOWLEDGMENT

The work is supported by NSF grant 10471091 of China.

Notes

^#Communicated by B. Allison.