JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2022, Vol. 57 ›› Issue (12): 71-74.doi: 10.6040/j.issn.1671-9352.0.2021.724

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First cohomology of W(2)with coefficients in Kac modules

DING Ya-zhou, WANG Shu-juan*   

  1. School of Mathematical Sciences, Heilongjiang University, Harbin 150080, Heilongjiang, China
  • Published:2022-12-05

Abstract: Over a field of characteristic p>2, the first cohomology of Witt-type Lie superalgebra W(2)with coefficients in two classes of Kac modules is determined. That the first cohomology spaces of W(2)with coefficients in K(2ξ2)and K(ξ12)are 1-dimensional and 0-dimensional respectively is showed.

Key words: Witt-type Lie superalgebra W(2), Kac module, derivation, cohomology

CLC Number: 

  • O152.5
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