${\mathbb{Z}}_2\times {\mathbb{Z}}_2$ generalizations of infinite dimensional Lie superalgebra of conformal type with complete classification of central extensions

Abstract

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.

arXiv comment19 pages, no figure, Revision in Section 2 and 3. Some new references

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Cited by in corpus (4)

• ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$-graded mechanics: the quantization
• A classification of lowest weight irreducible modules over ${\mathbb{Z}}_2^2$-graded extension of $osp(1|2)$
• ${\mathbb{Z}}_2^2$-graded supersymmetry via superfield on minimal ${\mathbb{Z}}_2^2$-superspace
• Affine extensions of ${\mathbb{Z}}_2^2$-graded $osp(1|2)$ and Virasoro algebra