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Hi everyone

I have a notational question, which is written usually in papers, but I can not figure it out what could be. Let $M$ be an $A$-module. I have seen this notation $$M^{\otimes -n}$$

I think this would mean $(Hom_A(M,A))^{\otimes n}$, but in the other way this can be denoted by $((M^*)^{\otimes n}$. Is this a standard notation?

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    $\begingroup$ That notation is usually used to mean your first option when the module is invertible. The only way to know what the author of those papers meant is to actually tell us what papers you are reading, though. $\endgroup$
    – Mariano Suárez-Álvarez
    Commented May 19, 2011 at 13:31
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    $\begingroup$ (The reason one prefers the notation $M^{\otimes -n}$ to $(M^*)^{\otimes n}$ is, first and most importantly, that it is considerably less cumbersome, but it also allows you to write things like $\bigoplus_{n\in\mathbb Z}M^{\otimes n}$ which would otherwise need notational circumlocutions.) $\endgroup$
    – Mariano Suárez-Álvarez
    Commented May 19, 2011 at 14:00
  • $\begingroup$ I retagged this question because a discussion on meta suggested they wanted to get rid of the generic "algebra" tag: tea.mathoverflow.net/discussion/1071/… $\endgroup$
    – David White
    Commented Jun 28, 2011 at 13:43

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