We will discuss representations of the Smith algebra which are free of finite rank over a subalgebra which plays a role analogous to that of the (enveloping algebra of the) Cartan subalgebra of the simple Lie algebra 𝔰𝔩2. In the case of rank 1 we obtain a full description of the isomorphism classes, a simplicity criterion, and a combinatorial algorithm to produce all composition series and the multiplicities of the simple factors.
This is joint work with V. Futorny (SUSTech & USP) and E. Mendonça (Lyon & USP).
This video is part of the European Non-Associative Algebra Seminar series.
