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Titlebook: Differential Geometry and Lie Groups; A Second Course Jean Gallier,Jocelyn Quaintance Textbook 2020 Springer Nature Switzerland AG 2020 Dif

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Clifford Algebras, Clifford Groups, and the Groups ,(,) and ,(,),roup .(.) is simply connected (a fact that it is not so easy to prove without some machinery), whereas .(.) is not simply connected. Intuitively speaking, .(.) is more twisted than .(.). In fact, we will see that .(.) is a double cover of .(.).
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https://doi.org/10.1007/978-3-7985-1888-9Tensors are creatures that we would prefer did not exist but keep showing up whenever multilinearity manifests itself.
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Exterior Tensor Powers and Exterior Algebras,In this chapter we consider . (also called .) multilinear maps and . (also called .), denoted .. In many respects alternating multilinear maps and exterior tensor powers can be treated much like symmetric tensor powers, except that sgn(.) needs to be inserted in front of the formulae valid for symmetric powers.
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Differential Geometry and Lie Groups978-3-030-46047-1Series ISSN 1866-6795 Series E-ISSN 1866-6809
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