In
mathematics, particularly in
abstract algebra, a
semigroup with involution or a
*-semigroup is a
semigroup equipped with an
involutive anti-automorphism, which—roughly speaking—brings it closer to a
group because this involution, considered as
unary operator, exhibits certain fundamental properties of the operation of taking the inverse in a group: uniqueness, double application "cancelling itself out", and the same interaction law with the binary operation as in the case of the group inverse. It is thus not a surprise that any group is a semigroup with involution. However, there are significant natural examples of semigroups with involution that are not groups.