Date of Defense
Joseph Buckley, Mathematics
This paper focuses on the group ring Z2Cp (p is a prime) in representation theory. The central problem is to decompose Z2Cp as a direct sum of fields by elementary methods, without using high powered representation theory. We consider two main approaches: (1) using orthogonal idempotents and (2) using the factorization of xp - 1 in Z2[x]. From this central problem, many smaller problems are explored. Among them are: finding all of the idempotents of the group ring, finding the irreducible polynomial factorization of xp - 1, finding the orthogonal basis of idempotents, and solving the problem completely for specific primes. Some of these questions are answered completely while others are investigated and left open.
Buczkowski, Peter, "Exploring Z2Cp: Using Idempotents, Polynomials, and o(2)" (1999). Honors Theses. 261.
Honors Thesis-Campus Only