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Mathematics
Linear and Abstract Algebra
Definition of Super Lie Module
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[QUOTE="fresh_42, post: 6600512, member: 572553"] I get the following equations \begin{align} [A.U_1,B.U_2]&=A.[U_1,B.U_2]\\&=(-1)^{|U_1||B.U_2|}A.[B.U_2,U_1]\\&=(-1)^{|U_1||B.U_2|}A.B.[U_2,U_1]\\&=(-1)^{|U_1||B.U_2|}(-1)^{|U_2||U_1|}A.B.[U_1,U_2]\\ &=(-1)^{|U_1||B|}A.B.[U_1,U_2]\\[6pt] [A.U_1,B.U_2]&=(-1)^{|A.U_1||B.U_2|}[B.U_2,A.U_1]\\&=(-1)^{|A.U_1||B.U_2|}(-1)^{|U_2||A|}B.A.[U_2,U_1]\\ &=(-1)^{|A||B|+|U_1||B|}B.A.[U_1,U_2]\\&=(-1)^{|U_1||B|}A.B.[U_1,U_2] \end{align} but have difficulties checking yours. I used the first result from (24) to (25) and the fact that we are only allowed to pull out the "scalar" at the first position of the bracket. [/QUOTE]
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Linear and Abstract Algebra
Definition of Super Lie Module
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