THE LOEWY STRUCTURE OF CERTAIN FIXPOINT ALGEBRAS, PART II

Year 2021, Volume: 30 Issue: 30, 16 - 65, 17.07.2021

T. Breuer L. L. Hethelyı E. Horvath B. Kulshammer

https://doi.org/10.24330/ieja.969577

Abstract

In Part I of this paper, we introduced a class of certain algebras of finite dimension over a field.
All these algebras are split, symmetric and local. Here we continue to investigate their Loewy structure.
We show that in many cases their Loewy length is equal to an upper bound established in Part I,
but we also construct examples where we have a strict inequality.
The algebras considered here include certain rings of fixpoints
under the action of particular finite groups.
Thus we consider the results in this paper as a contribution to
the general theory of fixpoint rings.

Keywords

Fixpoint algebra, symmetric algebra, Jacobson radical, Loewy length

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