ℤ2 × ℤ2-Generalizations of Infinite-Dimensional Lie Superalgebra of Conformal Type with Complete Classification of Central Extensions

We introduce a class of novel ℤ × ℤ-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 ℤ × ℤ-graded color superalgebras is presented. It turns out that infinitely many members of the class have nontrivial extensions. We also demonstrate that the color superalgebras (with and without central extensions) have adjoint and superadjoint operations