Linear representation theory of cyclic group:Z4
This article gives specific information, namely, linear representation theory, about a particular group, namely: cyclic group:Z4.
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This article gives information on the linear representation theory of cyclic group:Z4, the cyclic group of order four.
|degrees of irreducible representations over a splitting field|| 1,1,1,1|
maximum: 1, lcm: 1, number: 4, sum of squares: 4
|Schur index values of irreducible representations over a splitting field||1,1,1,1|
|smallest ring of realization (characteristic zero)||, same as , ring of Gaussian integers. Quadratic integral extension of|
|smallest field of realization (characteristic zero)||, same as . Cyclotomic quadratic extension of .|
|condition for a field to be a splitting field||Characteristic not two, and contains a square root of , i.e., a primitive fourth root of unity. Equivalently, the polynomial splits.|
|degrees of irreducible representations over a field not a splitting field (includes case of , the field of real numbers, and , the field of rational numbers)||1,1,2|
|smallest size splitting field||field:F5, i.e., the field with five elements.|
|Family name||Parameter values||General discussion of linear representation theory of family|
|finite cyclic group||4||linear representation theory of finite cyclic groups|