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How to multiply two groups

  1. Nov 20, 2007 #1
    Everyone must be familiar with U(1),SU(2) and SU(3) Lie groups in particle physics .
    But how does one define the multiplication of two groups of different dimensions
    aka SU(2) X U(1) or SU(3) X SU(2) X U(1).
  2. jcsd
  3. Nov 20, 2007 #2

    matt grime

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    You aren't multiplying them. That is the direct product of the groups. Give two groups the direct product GxH is the set of all pairs (g,h) g in G, h in H with the natural composition

  4. Nov 20, 2007 #3


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    It's also the direct sum. If ever you encounter the notation [tex]\bigoplus_{i=1}^n G_i[/tex], this is what it means. Take the cartesian product of the G_i and give them a group structure by defining the binary operation as in matt grime's post. (g1,...,gn)(g1',...,gn'1)=(g1g1',...,gngn')
    Last edited: Nov 20, 2007
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