The first cohomology of D(2,1;\alpha) with coefficients in baby Verma modules
Shuang Lang, Wende Liu, Shujuan Wang
TL;DR
This paper computes the first cohomology group of the Lie superalgebra D(2,1;) with coefficients in baby Verma modules over a field of characteristic p > 3, by analyzing outer superderivations.
Contribution
It provides the first explicit calculation of the first cohomology for D(2,1;) with baby Verma modules in characteristic p > 3, revealing new structural insights.
Findings
Determined the outer superderivations of D(2,1;)
Calculated the first cohomology group with baby Verma modules
Enhanced understanding of Lie superalgebra cohomology in positive characteristic
Abstract
Over a field of characteristic p > 3, the first cohomology group of Lie superalgebra D(2,1;\alpha) with coefficients in baby Verma modules is determined by calculating the outer superderivations of D(2,1;\alpha).
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Advanced Algebra and Geometry