NOVELTY - The piperazine derivative (A) is novel.    USE - For producing cross-linked type polymer which is used for non-aqueous gel-form ionic conductive composition used in lithium ion battery and electrochemical elements such as solar cell, capacitor, sensor, chemiluminescent display device or liquid crystal display element (all claimed).    ADVANTAGE - The gel-form ionic conductive composition is stable for long period of time also in the presence of an electrolyte which gelatinize in the electrolyte liquid and produce hydrofluoric acid and lithium hexafluorophosphate. An electrochemical element having high property is obtained using the gel form ionic conductive composition.    DETAILED DESCRIPTION - The piperazine derivative of formula (A) is novel.    R1 = hydrogen, (un)substituted 1-18C alkyl, or (un)substituted 6-20C aryl; and    R2 = (un)substituted 1-18C alkylene, (un)substituted, optionally saturated 6-20C cycloalkylene, (un)substituted 6-20C arylene, (un)substituted 7-21C aryl alkylene, (un)substituted 7-21C arylene alkylene, (un)substituted 8-22C arylene bis(alkylene) group, 1-30C heteroatom containing organic group having 1-6 heteroatoms, dialkyl (poly)silylene group, diaryl (poly)silylene group or bivalent group induced from polyacrylate or polymethacrylate, or direct bond; and    n = 1-100.    INDEPENDENT CLAIMS are included for the following:    (i) linear polymer having two hydrosilyl groups at the terminal, which is a linear copolymer obtained by addition reaction of the piperazine derivative with compound of formula (B).    R3 = (un)substituted 1-18C alkyl, (un)substituted 7-21C aralkyl or (un)substituted 6-20C aryl;    R4 = (un)substituted 1-18C alkylene, (un)substituted 6-20C arylene, (un)substituted 7-21C aryl alkylene, dialkyl (poly)silylene group, diaryl (poly) silylene group, dialkyl silylene bis(alkylene) group or direct bond;    Z2 = bivalent connection group, group induced from 1-100C heteroatom containing organic group having 1-50 heteroatoms, benzene polycarboxy group, phosphoric acid group, polyacrylate or polymethacrylate disubstituted by divalent silicon atom, (un)substituted 1-18C alkylene, (un)substituted 6-20C arylene or direct bond;    (ii) cross-linked type copolymer obtained by reacting the linear polymer having at least three ethylenic double bonds with compound of formula (D).    R6 = H, (un)substituted 1-18C alkyl, or (un)substituted 6-20C aryl;    R7 = 1-30C heteroatom containing organic group having 1-6 heteroatoms, (un)substituted 1-18C alkylene, (un)substituted 6-20C arylene, (un)substituted 7-21C aryl alkylene or direct bond;    Z3 = connection group with same valence as n1, group induced from 1-100C heteroatom containing organic group having 1-50 heteroatoms, benzene polycarboxy group, phosphoric acid group, oxyphosphoric acid group, polyacrylate or polymethacrylate, 1-18C alkane poly yl group, 6-20C multivalent aromatic carboxylic group, 1-12C alkane polyoxygroup, silicon atom, monosubstituted trivalent silicon atom, 1-300C aliphatic group or direct bond;    n1 = 3 or more;    R8 = (un)substituted 1-18C alkyl or (un)substituted 6-20C aryl;    R9 = R7;    Z4 = connection group with same valence as n1, group induced from 1-100C heteroatom containing organic group having 1-50 heteroatoms, benzene polycarboxy group, phosphoric acid group, oxyphosphoric acid group, polyacrylate or polymethacrylate, 1-18C alkylene group, 1-18C alkynyl group, 6-20C multivalent aromatic carboxylic group, 1-12C alkane polyoxy group, silicon atom, monosubstituted trivalent silicon atom, 1-300C aliphatic group or direct bond;    a = 0-3; and    n2 = 2-30;    (iii) non-aqueous gel-form ionic conductive composition which comprises the cross-linked type copolymer and electrolyte;    (iv) battery which comprises the gel-form non-aqueous ionic conductive composition;    (v) electroconductive element which comprises the gel-form non-aqueous ionic conductive composition; and    (vi) manufacture of battery or electrochemical element.    DESCRIPTION OF DRAWING(S) - The figure is a mass spectrum chart of compound (A-3). (Drawing includes non-English language text).