Representations of Spin(4), Spin(2,2) and Spin(3,1)
Abstract
In this essay we present an outer product on R6, and we show that R6 with this outer product can take three kinds of Lie brackets. We prove that R6 with these Lie brackets take the structures of so(4), so(2,2) and so(3,1). We also deduce a 4-dimensional submanifold of R6 with an almost complex structure.
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