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Are there some books or papers about the general definition of traces:

If $\mathscr{A}$ is an associative algebra over $K$ then the space of traces is the set of all linear functionals $\tau:\mathscr{A}\to K$ which satisfy $\tau(\mathcal{A}\mathcal{B})=\tau(\mathcal{B}\mathcal{A})$ for all $\mathcal{A},\mathcal{B}\in\mathscr{A}$.

Thanks.

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  • $\begingroup$ This is the dual of the 0th Hochschild homology of $A$, which gives a way to find a lot of references using Google. E.g. one is Loday's book "Cyclic homology." $\endgroup$
    – Peter Samuelson
    Commented Apr 3, 2018 at 14:51

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