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Advances in Applied Clifford Algebras

, Volume 10, Issue 2, pp 267–296 | Cite as

ON FRT– CLIFFORD ALGEBRAS

  • I. Heckenberger
  • A. Schüler
Original Paper

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.

MSC 2000

81R50 15A66 

Keywords.

q-Clifford algebra Drinfeld-Jimbo algebra spin representation 

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Copyright information

© Birkhäuser Verlag, Basel 2006

Authors and Affiliations

  1. 1.Mathematisches InstitutUniversität LeipzigLeipzigGermany

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