NOVELTY - A conductor electrolyte (C1) comprises a cation added to polymer having side chain consisting of alkylene unit and a functional group having coordination ability with respect to the cation. The alkylene unit and functional group are bonded to main polymer chain through an organic group.    USE - For manufacturing lithium secondary battery (claimed) useful for electric power supplies for e.g. electric automobiles; electric bicycles; personal computers; cellular phones; digital cameras; camcorders; portable minidisc players; personal digital assistants; wrist watches; radios; electronic personal organizers; electric tools; vacuum cleaners; toys; elevators; robots for emergency purposes; walking-aid machines for healthcare purposes; wheelchairs for healthcare purposes; moving beds for healthcare purposes; emergency electric supplies; load conditioners; electric power storage systems such as rechargeable batteries for household use; as dispersed power sources for household and regional use; and also useful as power supplies for military or space-exploration.    ADVANTAGE - The organic group having a functional group, which is a ligand coordinated to a lithium ion, is bound to a polymer main chain as a polymer side chain that is considerably shorter than the polymer main chain, enhances the mobility of the organic group than that of the polymer main chain, thus motion of the side chain reduces the activation energy generated upon conduction of a lithium ion to a similar functional group of the adjacent side chain and provides excellent temperature dependence of the ionic conductivity. The lithium battery manufactured with the polymer electrolyte is easily mounted on electric equipment for electric power supplies. Since no electrolytic fluid is used in the battery, the safety level is enhanced and it eliminates the requirement of protection circuit. The performance levels of battery is maintained at low temperature (not different from that at room temperature) and fluid does not leak at high temperatures, thus are used in a wide temperature range.    DETAILED DESCRIPTION - A conductor electrolyte (C1) comprises a cation added to polymer having side chain consisting of alkylene unit and a functional group having coordination ability with respect to the cation. The alkylene unit and functional group are bonded to main polymer chain through an organic group. The side-chain has a polymer structural unit of formula Rp-(Y-R1-Z)m (I).    Rp=an organic group obtained via polymerization of a compound containing polymerizable unsaturated linkages or a polymerized organic group containing C, H, N or O;    m=smaller than the polymerization degree of Rp;    Y=absent or organic group that binds to Rp;    R1=1-10C alkylene group that allows Y to bind to Z;and    Z=functional group having coordination ability with respect to a cation.    Provided that Z form a coordination bond with a cation. The polymer electrolyte composition comprises a cation added to a polymer having a side chain consisting of R1 and Z binding through Y to a polymer main chain consisting of Rp. INDEPENDENT CLAIMS are included for the following:    (1) a lithium secondary battery comprising a positive electrode having a positive electrode active material that can intercalate and deintercalate lithium and a negative electrode having a negative electrode active material that can intercalate and deintercalate lithium that are rolled or laminated via an interposing polymer electrolyte, where the polymer electrolyte comprises the cationic conductor (C1); and    (2) a precursor of a side-chain-type polymer of formula R-Y-R1a-O-CO-O-R2a (II).    R=organic group having polymerizable unsaturated linkages;    Y'=organic group that binds to R;    R1a=1-10C alkylene group that allows Y' to bind to a carbonate group;and    R2a=an organic group that binds to an end of the carbonate group.    Provided that the carbonate group is a functional group having coordination ability with respect to cation and forms coordination bond with the cation. The polymer structure comprises a functional group composed of R1 and carbonate group constitute the side chain.