Re: Wald's Isomorphism between V and V*

[Mike_Fontenot]

[[Mod. note -- I mistakenly deleted this article's References: headers
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I apologise to the author and other readers for this, and for the ensuing
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-- jt]]

Theo Wollenleben wrote:
> Mike_Fontenot schrieb:
>
>> I also like to be able to make explicit the difference between a MAP
>> itself, versus the target of a map (a number). I do that by adding a
>> subscript to a post-index, when I intend that post-index to represent
>> a specific value for the argument. (And I also use the same idea for
>> pre-indices). For example,
>>
>> V{sup a}
>>
>> is a MAP from duals to numbers, whereas
>>
>> V{sup a0}
>>
>> is a number, produced when the argument to V is the specific dual
>> {sup a0}W. I.e.,
>>
>> V( {sup a0}W ) = V{sup a0}.
>>
>
> With the [above] you miss your goal, "to preserve the idea that the
> meaning of my indices wouldn't depend on Latin vs Greek vs numeral".
> Indices with subscripts in your notation are like Greek indices in
> Wald's notation.
>
No, Greek indices are reserved for COEFFICIENTS in Wald's notation. In
my notation, coefficients are always written with a lower-case root
letter, whereas tensors (including vectors and duals) are always written
with an upper-case root letter. My previous posting didn't refer to
coefficients at all.

Mike Fontenot