Primitive idempotents in central simple algebras over <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:msub><mml:mrow><mml:mi mathvariant="double-struck">F</mml:mi></mml:mrow><mml:mrow><mml:mi>q</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math> with an application to coding theory

Primitive Central Idempotents of Nilpotent Group Algebras

We exhibit the primitive central idempotents of a semisimple group algebra of a finite nilpotent group over an arbitrary field (without using group characters), examining the abelian case separately. Our result extends and improves the main result in [1].

Central Idempotents in Group Algebras

Central Bank Independence and Central Bank Conservatism: Theory with an Application to Iran

New monetary literatures widely concentrates on the importance of institutional arrangements in the effectiveness of monetary policy. The debate regarding the optimal institutional design of central banks, independence and conservatism are usually considered to be the most important ingredients for a stable and successful monetary policy. Therefore, the purpose of this study is to deal with the...

Computing the dimension of ideals in group algebras, with an application to coding theory

Abstract We study the problem of computing the dimension of a left/right ideal in a group algebra F[G] of a finite group G over a field F, by relating the dimension to the rank of an appropriatematrix, originating from a regular right/left representation of G. In particular, the dimension of a principal ideal is equal to the rank of the matrix representing a generator. From this observation, we...

Primitive central idempotents of finite group rings of symmetric groups

Let p be a prime. We denote by Sn the symmetric group of degree n, by An the alternating group of degree n and by Fp the field with p elements. An important concept of modular representation theory of a finite group G is the notion of a block. The blocks are in one-to-one correspondence with block idempotents, which are the primitive central idempotents of the group ring FqG, where q is a prime...