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Unfortunately there seems to be a misprint in the paper I'm reading which is an introduction to clifford algebra, it says:(I highlighted in red possible misprint, either one of them has to be true misprint if you know what I mean)

The Clifford algebra C(V) is isomorphic to the tensor algebra Lambda(V) and is therefore a 2^{dim(V)} dimensional vector space with generators blah blah blah...

Now, I know C(V) is defined as T(V)/I with you know what "I" so I'm wondering how can there be isomorphism between C(V) and T(V) but on the other hand dimension 2^{dim(V)} is indeed dimension of tensor algebra right? Also the author said tensor algebra but then wrote Lambda...-_-

I'm confused~~

The Clifford algebra C(V) is isomorphic to the tensor algebra Lambda(V) and is therefore a 2^{dim(V)} dimensional vector space with generators blah blah blah...

Now, I know C(V) is defined as T(V)/I with you know what "I" so I'm wondering how can there be isomorphism between C(V) and T(V) but on the other hand dimension 2^{dim(V)} is indeed dimension of tensor algebra right? Also the author said tensor algebra but then wrote Lambda...-_-

I'm confused~~

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