Dr Surinder Kaur, Assistant Professor at the Department of Mathematics is making significant contributions to the mathematical community and SRMAP’s research wing, her research on understanding the group rings and addressing challenges such as the isomorphism problem for group algebra through her project has earned her a funding of ₹ 4.28 lakh from the prestigious National Board for Higher Mathematics (NBHM). Dr Kaur’s impressive research work has become a source of inspiration to many. Given below are some details on her project titled, “On the group rings, their unit groups and some related questions”
A Brief Description of the Project
In this project, we aim at obtaining the structure and generators of the unit group of some group rings with a focus on answering the normal complement problem for them. Our further goal is to solve the celebrated isomorphism problem for group algebras of certain classes of groups, especially the twisted version of this problem for group algebras of nilpotency class at least 3. We also plan to look into certain questions in the representation theory of association schemes that are driven by what happens for group algebras.
Explanation of Research Objectives in layperson’s terms
In the last century, the work of E. Noether, F.G. Frobenius and R. Brauer have established that group rings play a central role in the development of representation theory. Further investigations indicated that these objects also have a great influence on the study of other areas of Mathematics like algebraic number theory, algebraic K-theory and algebraic topology. Moreover, the vital role it has played in the recent development of homological algebra and algebraic coding theory is worth acknowledgement.