Introduction:
Hydrolysis is a chemical reaction that involves the breaking of chemical bonds in a compound by the addition of water. Some compounds readily undergo hydrolysis in water, while others do not. In this case, we need to determine which among the given species is not hydrolyzed in water.

Explanation:
Let's analyze each species and their hydrolysis behavior in water:

a. P4O10 (tetraphosphorus decoxide):
P4O10 is a covalent compound that reacts vigorously with water to form phosphoric acid (H3PO4). The hydrolysis of P4O10 is an exothermic reaction and produces a large amount of heat. Therefore, P4O10 undergoes hydrolysis in water.

b. BaO2 (barium peroxide):
BaO2 is an ionic compound that is stable in water. It does not readily undergo hydrolysis and remains as BaO2 in water. Therefore, BaO2 is not hydrolyzed in water.

c. Mg3N2 (magnesium nitride):
Mg3N2 is an ionic compound that reacts with water to produce magnesium hydroxide (Mg(OH)2) and ammonia gas (NH3). This reaction is an example of hydrolysis, where the water molecules split the compound into its constituent ions. Therefore, Mg3N2 undergoes hydrolysis in water.

d. CaC2 (calcium carbide):
CaC2 is a covalent compound that reacts with water to produce acetylene gas (C2H2) and calcium hydroxide (Ca(OH)2). This reaction is also an example of hydrolysis, where water molecules break the chemical bonds in the compound. Therefore, CaC2 undergoes hydrolysis in water.

Conclusion:
Among the given species, BaO2 is the compound that is not hydrolyzed in water. P4O10, Mg3N2, and CaC2 undergo hydrolysis in water, resulting in the formation of other compounds.