We introduce a class of novel $\mathbb{Z}_2 \times \mathbb{Z}_2$-graded color superalgebras of infinite dimension. It is done by realizing each member of the class in the universal enveloping algebra of a Lie superalgebra which is a module extension of the Virasoro algebra. Then the complete classification of central extensions of the $\mathbb{Z}_2 \times \mathbb{Z}_2$-graded color superalgebras is presented. It turns out that infinitely many members of the class have non-trivial extensions. We also demonstrate that the color superalgebras (with and without central extensions) have adjoint and superadjoint operations.

中文翻译：

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ℤ2 × ℤ2-具有中心外延完全分类的保形型无限维李超代数的推广

我们介绍了一类新颖的$\mathbb{Z}_2 \times \mathbb{Z}_2$-graded 无限维彩色超代数。它是通过在李超代数的泛包络代数中实现类的每个成员来完成的，李超代数是 Virasoro 代数的模块扩展。然后给出了$\mathbb{Z}_2 \times \mathbb{Z}_2$-graded 颜色超代数的中心扩展的完整分类。事实证明，该类的无限多成员具有非平凡的扩展。我们还证明了彩色超代数（有和没有中心扩展）具有伴随和超伴随运算。