Structure of a semisimple dihedral group algebra | Zendy

I Gradeva | Zendy; Yordan Epitropov | Zendy

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Structure of a semisimple dihedral group algebra

Author(s) -

I Gradeva,

Yordan Epitropov

Publication year - 2019

Publication title -

iop conference series materials science and engineering

Language(s) - English

Resource type - Journals

eISSN - 1757-899X

pISSN - 1757-8981

DOI - 10.1088/1757-899x/618/1/012090

Subject(s) - dihedral group , dihedral angle , mathematics , group (periodic table) , order (exchange) , group algebra , field (mathematics) , algebra over a field , pure mathematics , physics , hydrogen bond , finance , quantum mechanics , molecule , economics

Let K be an arbitrary field, whose characteristic does not divide the order of the dihedral group D 2m of order 2 m , where m is odd. In this paper we examine the structure of the semisimple dihedral group algebra KD 2m . For this purpose, we find a complete system of minimal central orthogonal idempotents of the group algebra. Through it we define the minimal components of KD 2m and its Wedderburn decomposition. The results we get are as general as possible, i.e. without requiring the field to be finite.

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