Copyright
Jan E. GrabowskiPublished On
2025-09-22Page Range
pp. 89–108Language
- English
Print Length
20 pages
3. Representations
- Jan E. Grabowski (author)
It is very common to say that groups often arise as symmetries. The subtle but important shift from “what group encodes the symmetries of this object?” to “which objects does this group give symmetries of?” moves us from the structure theory of groups to their representation theory. We also examine representations of algebras and quivers.
Contributors
Jan E. Grabowski
(author)Jan Grabowski is an experienced researcher and educator in mathematics, with over 20 years’ experience of both, and currently holds the position of Professor of Algebra at Lancaster University. Jan has a strong research track record of publications in algebra and related topics, both as a single author and collaboratively. He has taught courses at Oxford and Lancaster across a range of levels and has been teaching abstract algebra for the majority of this time, including covering aspects of the material in the book in courses at both institutions. Jan has had recognition for his teaching, including a teaching prize at Oxford, obtaining a Postgraduate Certificate in Academic Practice and being awarded Senior Fellowship of the Higher Education Academy. He has championed innovation in teaching by presenting a mature exposition of ‘how mathematicians really think about these things’ as compared with other approaches that often defer more advanced ideas or techniques, rather than encouraging students to engage with challenging ideas early and repeatedly.