??? algebra with anti-involution * with the *-invariant part associative and commutative .... ??? as module with quadratic form and anti-commutative bilinear operation ??? ....

hmmm .... ??? "qfs" as special case .... ????? ...... ??? "killing form" ???? ..... ??? possible extra laws to impose here .... ???? "killing law" ??? ..... ???? leibniz identity .... ??? .....

?? "enveloping algebra" .... ????? ..... ???? ..... exterior algebra .... ???? .....

????? .......

?? bit about axiomatic (?? ...) characterization of cayley-dickson endofunctor ... ?? incorporating some of above ideas ??? .....