Il’inskij, K. N.; Stepanenko, A. S. \(q\)-deformed superspace and \(q\)-extended supersymmetric Hamiltonian with arbitrary superpotential. (English. Russian original) Zbl 0943.58005 J. Math. Sci., New York 94, No. 4, 1611-1619 (1999); translation from Zap. Nauchn. Semin. POMI 235, 260-272 (1996). The authors consider one of the possible generalizations of supersymmetry (SUSY). For this purpose, they state the \(q\)-superspace formalism and construct the \(q\)-supertransformation group on this \(q\)-superspace. After this, they begin with a standard action for a scalar \(d\)-dimensional real superfield and construct a \(q\)-extended supersymmetric Lagrangian for the component variables of the \(q\)-superfield. After the quantization procedure, the corresponding conserved quantities become \(q\)-supercharges. Reviewer: Viktor Abramov (Tartu) MSC: 58C50 Analysis on supermanifolds or graded manifolds 81R50 Quantum groups and related algebraic methods applied to problems in quantum theory 81T60 Supersymmetric field theories in quantum mechanics Keywords:\(q\)-deformed superspace; \(q\)-supertransformations × Cite Format Result Cite Review PDF Full Text: EuDML