Torsionfree representations of Smith algebras

Abstract: 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 $\mathfrak{sl}_2$. 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).

quantum algebrarings and algebras

Audience: researchers in the topic

European Non-Associative Algebra Seminar