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Within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism, we showthe existence of (i) a couple of off-shell nilpotent (i.e. fermionic) BRST andco-BRST symmetry transformations, and (ii) a full set of non-nilpotent (i.e.bosonic) symmetry transformations for an appropriate Lagrangian density thatdescribes the combined system of the free Abelian 3-form and 1-form gaugetheories in the physical four (3 + 1)-dimensions of the flat Minkowskianspacetime. We concentrate on the full algebraic structures of the abovecontinuous symmetry transformation operators along with a couple of very usefuldiscrete duality symmetry transformation operators existing in our four (3 +1)-dimensional (4D) field-theoretic model. We establish the relevance of thealgebraic structures, respected by the above discrete and continuous symmetryoperators, to the algebraic structures that are obeyed by the de Rhamcohomological operators of differential geometry. One of the highlights of ourpresent endeavor is the observation that there are no ``exotic'' fields withthe negative kinetic terms in our present 4D field-theoretic example for Hodgetheory.

Continuous and Discrete Symmetries in a 4D Field-Theoretic Model: Symmetry Operators and Their Algebraic Structures