The Temperley-Lieb algebra at roots of unity
The ascending sequences of finite dimensional algebras, given by relations (between generators) depending on one or several parameters, are considered. It is assumed that, for generic values of parameters, the algebras are semisimple. A systematic study is initiated of the structure of such algebras at the critical values of the parameters, where they cease to be semisimple. The Temperley-Lieb algebras are studied in detail; however, it is expected that the techniques used can be applied to other cases (Brauer algebras, Birman-Wenzl algebras). The main techniques used in the paper are: (i) the use of representation theory to obtain the algebraic identities which remain valid at critical values of parameters, (ii) spectral analysis for path idempotents.
ascending sequences of finite dimensional algebras
scientific article; zbMATH DE number 540668