ON FRT– CLIFFORD ALGEBRAS

Abstract.

We study the q-Clifford algebras

$$\hbox{Cl}_{{q}^{2}} (N, c^2)$$

, called FRT–Clifford algebras, introduced by Faddeev, Reshetikhin and Takhtajan. It is shown that

$$ \hbox{Cl}_{{q}^{2}} (N, c^2)$$

acts on the q-exterior algebra

$$ \Lambda(\hbox{O}^{N}_{{q}^{2}})$$

. Moreover, explicit formulas for the embedding of

$$ U_{{q}^{2}} (\mathcal{S} \mathcal{O}_{N})$$

into

$$ \hbox{Cl}_{{q}^{2}} (N, c^2) $$

and its relation to the vector and spin representations of

$$ U_{{q}^{2}} (\mathcal{S} \mathcal{O}_{N})$$

are given and proved.