ИСТИНА

It is shown that basic classical Lie superalgebras can be extended to Z_2х...xZ_2-graded superalgebras with the same even part of the Z_2-case. For this purpose, a Z_2x...xZ_2-graded bosonic algebra is introduced using a cliffonic dressing of an ordinary bosonic algebra. Some real forms of such Z_2x...xZ_2-superalgebras are considered. A new concept of Hermitian imaginary unit is introduced (the usual imaginary unit is an anti-Hermitian one).