I am reading the book "Lie superalgebras and enveloping algebras by Ian M.Musson"

The strange type $P(n)$ series of Lie superalgebras are defined only for $n \ge 2$ even though for $n = 1$ the definition makes perfect sense.

My question is, $n = 1$ case is not considered because this Lie superalgebra is actually belonged to earlier defined types and so in ordered to avoid overcounting? or $P(1)$ is not simple? (In this case, is it easy to find the Ideal?)

Thanks for your time.

I am reading the book "Lie superalgebras and enveloping algebras" by Ian M. Musson.

The strange type $P(n)$ series of Lie superalgebras are defined (§2.4.1, p. 17) only for $n \ge 2$ even though for $n = 1$ the definition makes perfect sense.

My question is, $n = 1$ case is not considered because this Lie superalgebra is actually belonged to earlier defined types and so in ordered to avoid overcounting? or $P(1)$ is not simple? (In this case, is it easy to find the Ideal?)

Thanks for your time.