Annual Seminar for Mathematics Research Scholars
Date: Friday, 06 October 2023
Time: 2:00 PM
Venue: Lecture Hall 801
Rewriting Theory and Basis theorems
Sadhanandh Vishwanath B.
Chennai Mathematical Institute.
06-10-23

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Abstract

When an algebraic structure (i.e., algebras, linear categories) A is presented using generators and relations, the size (dimension) of them is not immediately apparent. Even with seemingly innocent relations, it is possible that it was zero the entire time. Hence it is essential to have a basis for A.

It is often possible to find a set of monomials, i.e. elements that are expressed as words in the generators, which span the A, and which one expects is a basis. However, proving the linear independence of this set can be a challenging task.

In this talk, I will explain some rewriting theories, especially diamond lemmas, which provide a crucial technique for proving linear independence.