# Jacobson generators of the quantum superalgebra Uq[sl(n+1|m)] and Fock representations

@article{Palev2001JacobsonGO, title={Jacobson generators of the quantum superalgebra Uq[sl(n+1|m)] and Fock representations}, author={Tchavdar D. Palev and N I Stoilova and Joris Van der Jeugt}, journal={Journal of Mathematical Physics}, year={2001}, volume={43}, pages={1646-1663} }

As an alternative to Chevalley generators, we introduce Jacobson generators for the quantum superalgebra Uq[sl(n+1|m)]. The expressions of all Cartan–Weyl elements of Uq[sl(n+1|m)] in terms of these Jacobson generators become very simple. We determine and prove certain triple relations between the Jacobson generators, necessary for a complete set of supercommutation relations between the Cartan–Weyl elements. Fock representations are defined, and a substantial part of this paper is devoted to…

## 2 Citations

### Jacobson generators of (quantum) sl(n+1|m). Related statistics.

- Materials Science
- 2002

T.D. PALEV †, N.I. STOILOVA ‡ and J. VAN der JEUGT § † Institute for Nuclear Research and Nuclear Energy, Boul. Tsarigradsko Chaussee 72, 1784 Sofia, Bulgaria E-mail: tpalev@inrne.bas.bg ‡…

### Deformed Clifford Clq(n|m) and orthosymplectic Uq[osp(2n + 1|2m)] superalgebras and their root of unity representations

- Mathematics
- 2002

It is shown that the Clifford superalgebra Cl(n|m) generated by m pairs of Bose operators (odd elements) anticommuting with n pairs of Fermi operators (even elements) can be deformed to Clq(n|m) such…

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