A Generalization of Borcherds Algebra and Denominator Formula Original Research Article

We study generalized Lie superalgebras (an extension of Kacʹs generalized Lie superalgebras) and show that they are transformed forms ofL-graded Lie superalgebras for some abelian groupL. We then introduce a generalized Lie superalgebra version of the generalized Kac–Moody algebra (Borcherds algebra). Since it is a transformed Borcherds superalgebra, it has several properties similar to those of Borcherds superalgebra. For example, it is defined by similar relations and has a similar denominator formula and character formulas.