Event Details

Pure maths seminar: From exceptional to tau-exceptional sequences.

Finite dimensional algebras are often given as path algebras modulo an ideal I of relations. If I is zero, the algebra is so-called hereditary, and the representation theory of such algebras is quite well understood. One important tool is the notion of exceptional sequences, which provides a technique to identify descending sequences of module categories (= categories of representations) of decreasing rank, sitting nicely inside a given module category. "Nicely" here means: kernels, cokernels and exact sequences should be preserved.

If the ideal I is non-zero, the classical theory of exceptional sequences is often not very helpful, since most algebras do not admit such sequences. In a series of papers with Eric J. Hanson and/or Bethany R. Marsh, we have developed a theory of tau-exceptional sequences, which is a natural generalization to this more general setting. We aim to explain some of the main ideas, features and shortcomings of this theory. In particular, we will illustrate a mutation operation for tau-exceptional sequences, which was introduced in a recent preprint, arxiv: 2402.10301.