Consider tri-linear forms, $\{A_{ijk}\}$ where $i=1,..,n_1$, $j=1,..,n_2$, $k=1,..n_3$, over a field of zero characteristic, up to the equivalence $A\to (U_1,U_2,U_3)(A)$, by three matrices. What is known about the classification? (Complete) invariants? Unlike the case of bi-linear forms, in general the classification has moduli.

I've found only an old paper of Thrall, dealing with partial cases. Is there some general (and more modern) exposition/introduction/lecture notes?

My particular question: for which triples $(n_1,n_2,n_3)$ is the classification discrete? (The obvious necessary condition, $n_1n_2n_3\le n^2_1+n^2_1+n^2_3$, is certainly not sufficient.)

Consider tri-linear forms, $\{A_{ijk}\}$ where $i=1,\dotsc,n_1$, $j=1,,n_2$, $k=1,\dotsc n_3$, over a field of zero characteristic, up to the equivalence $A\to (U_1,U_2,U_3)(A)$, by three matrices. What is known about the classification? (Complete) invariants? Unlike the case of bi-linear forms, in general the classification has moduli.

I've found only an old paper On Projective Equivalence of Trilinear Forms of Thrall, dealing with partial cases. Is there some general (and more modern) exposition/introduction/lecture notes?

My particular question: for which triples $(n_1,n_2,n_3)$ is the classification discrete? (The obvious necessary condition, $n_1n_2n_3\le n^2_1+n^2_1+n^2_3$, is certainly not sufficient.)

Consider tri-linear forms, $\{A_{ijk}\}$ where $i=1,..,n_1$, $j=1,..,n_2$, $k=1,..n_3$, over a field of zero characteristic, up to the equivalence $A\to (U_1,U_2,U_3)(A)$, by three matrices. What is known about the classification? (Complete) invariants? Unlike the case of bi-linear forms, in general the classification has moduli.

I've found only an old paper of Thrall, dealing with partial cases. Is there some general (and more modern) exposition/introduction/lecture notes?

My particular question: for which triples $(n_1,n_2,n_3)$ is the classification discrete?

Consider tri-linear forms, $\{A_{ijk}\}$ where $i=1,..,n_1$, $j=1,..,n_2$, $k=1,..n_3$, over a field of zero characteristic, up to the equivalence $A\to (U_1,U_2,U_3)(A)$, by three matrices. What is known about the classification? (Complete) invariants? Unlike the case of bi-linear forms, in general the classification has moduli.

I've found only an old paper of Thrall, dealing with partial cases. Is there some general (and more modern) exposition/introduction/lecture notes?

My particular question: for which triples $(n_1,n_2,n_3)$ is the classification discrete? (The obvious necessary condition, $n_1n_2n_3\le n^2_1+n^2_1+n^2_3$, is certainly not sufficient.)