Physics Glossary Definition (English)
Abelian Defined
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"(see above aside) This describes an algebraic operation (multiplication, addition, division, subtraction, etc.). If the operation is Abelian, then the elements commute. For example regular multiplication commutes: 3x4 = 4x3 = 12. Addition also commutes: 3+4 = 4+3 = 7. There are mathematical elements (matrices) which do not commute under multiplication. (If A and B are matrices, then A times B does not equal B times A.) Operations which are different when the elements are exchanged (which do not commute) are called non-Abelian. These ideas are named for the developer, Niels Abel."
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