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On the relation of Manin's quantum plane and quantum Clifford algebras

Bertfried Fauser
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Abstract

One particular approach to quantum groups (matrix pseudo groups) provides the Manin quantum plane. Assuming an appropriate set of non-commuting variables spanning linearly a representation space one is able to show that the endomorphisms on that space preserving the non-commutative structure constitute a quantum group. The non-commutativity of these variables provide an example of non-commutative geometry. In some recent work we have shown that quantum Clifford algebras --i.e. Clifford algebras of an arbitrary bilinear form-- are closely related to deformed structures as q-spin groups, Hecke algebras, q-Young operators and deformed tensor products. The natural question of relating Manin's approach to quantum Clifford algebras is addressed here. Some peculiarities are outlined and explicite computations using the Clifford Maple package are exhibited. The meaning of non-commutative geometry is re-examined and interpreted in Clifford algebraic terms.

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Bertfried Fauser. 2000-07-24. On the relation of Manin's quantum plane and quantum Clifford algebras. https://doi.org/10.1023/a%3A1022800705553

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