A Quantum commutative U-module algebra for U = anti-U(q) sl(2) at an even root of unity
Sep, 2008Citations per year
Abstract: (arXiv)
We show that the full matrix algebra Mat_p(C) is a quantum commutative U-module algebra for U=U_q sl(2), a quantum sl(2) group at the 2p-th root of unity. Mat_p(C) decomposes into a direct sum of projective U-modules P^+_n over odd n. In terms of generators and relations, this U-module algebra is described as the space of q-differential operators 'in one variable' with the relations D z = q - q^{-1} + q^{-2} z D and z^p = D^p = 0. These relations define a quantum, or 'parafermionic' statistics generalizing the fermionic commutation relations at p=2.- quantum algebra
- quantum group: SL(2)
- commutation relations
- algebra: representation
- operator: differential
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