TY - JOUR
AU - Epitropov, Yordan
AU - Gradeva, Ivanka
PY - 2022/05/28
Y2 - 2022/12/03
TI - Wedderburn Decomposition and Structure of a Semi-Simple Dihedral Group Algebra
JF - Novel Research Aspects in Mathematical and Computer Science Vol. 4
JA - NRAMCS-V4
VL -
IS -
SE - Chapters
DO - 10.9734/bpi/nramcs/v4/15764D
UR - https://stm.bookpi.org/NRAMCS-V4/article/view/7038
SP - 99-107
AB - <p>Let \(K\) be an arbitrary field, whose characteristic does not divide the order of the dihedral group \(D_{2 m}\) of order \(2 m\), where \(m\) is odd, and \(K D_{2 m}\) be the group algebra of \(D_{2 m}\) over the field \(K\). The structure of the semisimple dihedral group algebra \(K D_{2 m}\) is examined in this work. We find a complete system of minimal central orthogonal idempotents of the group algebra for this purpose. We define the simple components of \(K D_{2 m}\) and its Wedderburn decomposition through it. The results are as general as possible, i.e. they do not require a finite field.</p>
ER -