Let K be any field. In this paper we give a complete list of the indecomposable left injective module over the Jacobson algebra K, i.e., the free associative K-algebra on two (noncommuting) generators, modulo the single relation XY = 1. This is the natural continuation of the paper of the second two authors with Gene Abrams on the charaterization of the injective envelope of the simple modules over K.
INDECOMPOSABLE INJECTIVES OVER THE JACOBSON ALGEBRA
RICCARDO COLPI;ALBERTO TONOLO
2024
Abstract
Let K be any field. In this paper we give a complete list of the indecomposable left injective module over the Jacobson algebra K, i.e., the free associative K-algebra on two (noncommuting) generators, modulo the single relation XY = 1. This is the natural continuation of the paper of the second two authors with Gene Abrams on the charaterization of the injective envelope of the simple modules over K.
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