What is the meaning of det V and det V* in Generalised Complex geometry?

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SUMMARY

The discussion clarifies the notation "det V" and "det V*" in the context of Generalised Complex geometry, specifically referring to a real vector space V and its dual V*. The term "det V" is interpreted as the repeated wedge product \wedge^n V, where n is the dimension of the vector space V. This interpretation is crucial for understanding the determinant in the framework of Generalised Complex geometry as outlined in the thesis available at http://arxiv.org/abs/math/0401221v1.

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reginald
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Hi, I'm a reading a thesis on Generalised Complex geometry and it mentions an object " det V" and "det V*", for a real vector space V, and its dual V*. Could anyone tell me what this notation means? I've been unable to find anything mentioning a determinant of an entire vector space, so I'm fairly confused! The thesis I'm reading is http://arxiv.org/abs/math/0401221v1, and the det V first appears on page 11.
Thanks!
 
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If V is n-dimensional, it probably means the repeated wedge product [itex]\wedge^n V[/itex].
 

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