THE MULTIPLICATION ALGEBRA OF A B-SEMISIMPLE BARIC ALGEBRA

Abstract

In this paper we study the multiplication algebra M(A) of an arbitrary baric algebra A of finite dimension with idempotent element of weight 1. First, we prove that if A is a baric algebra, then its multiplication algebra is baric too. We give an example where the baric algebra A is b-semisimple, that is, in the baric sense, but its multiplication algebra M(A) is not b-semisimple. Then, we provide conditions under which this multiplication algebra is b-semisimple, when the baric algebra A is b-semisimple. We finish with a partial converse, that is, if M(A) is b-semisimple and A ² = A, then A is b-semisimple.

^*The author was sponsored by CAPES-PICD.

Keywords:

• 1991 Mathematics Subject Classification: 17D92

ACKNOWLEDGMENT

The authors thank the referee for his comments and suggestions that improved the presentation of this paper.

Notes

^*The author was sponsored by CAPES-PICD.