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On supermatrix idempotent operator semigroups. (English) Zbl 1044.47034

The author approaches some topics in supersymmetry by using concepts and methods from the theory of one-parameter operator semigroups. He introduces and investigates one-parameter semigroups of antitriangle idempotent supermatrices and superoperator semigroups. Operators which can be represented as a linear supermatrix function of the parameter \(t\) are called \(t\)-linear superoperators. It is shown that certain \(t\)-linear idempotent superoperators provide a non- exponential solution to an initial value problem.

MSC:

47D06 One-parameter semigroups and linear evolution equations
58A50 Supermanifolds and graded manifolds
81T60 Supersymmetric field theories in quantum mechanics
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