Automorphisms of Borcherds superalgebras and fixed point subalgebras

Let be a Borcherds superalgebra and let ω be a finite order automorphism of satisfying certain conditions. We prove that the fixed point subalgebra is equal to a Borcherds superalgebra. We also compute the trace of ω on from the twisted denominator identity of , and derive closed form formula for root multiplicities of .