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ON FRT– CLIFFORD ALGEBRAS (2000)

Heckenberger, I. ; Schüler, A.

Springer

Advances in applied Clifford algebras 10 (2000), S. 267-296

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ISSN: 1661-4909

Keywords: 81R50 ; 15A66 ; q-Clifford algebra ; Drinfeld-Jimbo algebra ; spin representation

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: 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.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/s00006-000-0008-9

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