The mathematics of Temperley-Lieb
by David Ridout
Abstract: The representation theory of finite-dimensional associative algebras is a classical subject, usually illustrated by the group algebras of finite groups. However, these are always semisimple in characteristic zero. The Temperley-Lieb algebras form a much more appealing case study for mathematical physicists as semisimplicity cannot be guaranteed even when working over the complex number field. This talk aims to introduce the (complex) Temperley-Lieb algebras and describe their representation theories, both semisimple and not, with the aid of pictures and examples. The term "quiver" will never be mentioned.
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