Cohomologies of Some Four-Dimensional Simple Jordan Superalgebras

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发表日期：

2025年1月1日

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J. A. Ramírez-Bermúdez,
F. A. Gómez-González

摘要

We calculate the second cohomology group for the four-dimensional simple Jordan superalgebra 𝒥osp_1|2(𝔽) by proving that its second cohomology group with coefficients in the regular representation is isomorphic to ${\mathbb{F}}\dot{+}0$ $F \dot{+} 0$ . We show (without proof) that for the four-dimensional simple Jordan superalgebra 𝒟_t with t ≠ 0, the superalgebra (V, f) of a superform with n = 1 and m = 1, and ℳ_1|1(𝔽)⁽⁺⁾ the respective second cohomology groups (with coefficients in the regular representation) are isomorphic to ${\mathbb{F}}\dot{+}0$ $F \dot{+} 0$ .