Question 7 — What extra relations should be added to Zn to make it finite-dimensional?

Definitions and mathematical statement

The question asks which additional relations should be imposed on the source's $Z_n$ so that the resulting object is finite-dimensional. The definition, presentation, coefficient field and range of $n$ are absent; $Z_n$ is not identified with a cyclic group or a guessed braid/Hecke algebra.

If $Z_n$ is the intended associative algebra over a field $k$, a precise version would seek explicit relations generating a two-sided ideal $I_n$ with $\dim_k(Z_n/I_n)<\infty$. This is conditional notation, not a recovered definition. The source gives no nonzero/proper-quotient or structure-preservation requirement: without such constraints, imposing relations that collapse the entire object may make the problem vacuous. The desired admissible quotient must therefore be specified before selecting relations.

Short English statement

Find admissible extra relations producing a finite-dimensional quotient of the missing object $Z_n$, with coefficients and nontriviality requirements fixed.

Sources

• Problems on Mapping Class Groups and Related Topics, edited by Farb, Question 7, supplied PDF page 323. https://www.math.uchicago.edu/~farb/papers/mcgbook.pdf. Recorded access 2026-07-29; extraction pdf-font-structure. The definition of $Z_n$ is absent.
• Local UnsolvedMath registry, data/unsolvedmath/problems.json, permanent ID $11000264$, exact source code catalogue entry. Its OPEN-TRIAGE summary speculates about braid/Hecke-type quotients without a supporting reference.