Institute for Radiophysics and Electronics (IRE), NAS of Ukraine,

12 Ak. Proskura Str., 61085, Kharkiv, UKRAINE

E-mail: kost@ire.kharkov.ua

**Osp(2/1;C) graded Lie algebra and its intended applications
to Yang-Mills theory**

**Abstract:**

We construct explicitly the grade star Hermitian adjoint representation
of osp(2/1;C) graded Lie algebra. Based on this a graded Yang-Mills field
strength is defined. Its even part coincides with the field strength of
the proper Lie subalgebra, su(2), of osp(2/1;C). We show that a pair of
Grassman-odd scalar fields can be treated as a constituent part of the
graded gauge potential on the equal footing with and ordinary (Grassman-even)
one-form with values in the proper Lie subalgebra of graded Lie algebra
osp(2/1;C). Action of gauge transformations on the defined field strength
and Baker-Campbell -Hausdorff formula are considered, some possibilities
of defining a meaningful variation principle are discussed.