TY - JOUR
T1 - Group inversion in certain finite-dimensional algebras generated by two idempotents
AU - Böttcher, A.
AU - Spitkovsky, I. M.
PY - 2012/12
Y1 - 2012/12
N2 - Invertibility in Banach algebras generated by two idempotents can be checked with the help of a theorem by Roch, Silbermann, Gohberg, and Krupnik. This theorem cannot be used to study generalized invertibility. The present paper is devoted to group invertibility in two types of finite-dimensional algebras which are generated by two idempotents, algebras generated by two tightly coupled idempotents on the one hand and algebras of dimension at most four on the other. As a side product, the paper gives the classification of all at most four-dimensional algebras which are generated by two idempotents.
AB - Invertibility in Banach algebras generated by two idempotents can be checked with the help of a theorem by Roch, Silbermann, Gohberg, and Krupnik. This theorem cannot be used to study generalized invertibility. The present paper is devoted to group invertibility in two types of finite-dimensional algebras which are generated by two idempotents, algebras generated by two tightly coupled idempotents on the one hand and algebras of dimension at most four on the other. As a side product, the paper gives the classification of all at most four-dimensional algebras which are generated by two idempotents.
KW - Finite-dimensional algebra
KW - Group inversion
KW - Idempotent
KW - Two projections
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U2 - 10.1016/j.indag.2012.08.006
DO - 10.1016/j.indag.2012.08.006
M3 - Article
AN - SCOPUS:84870691940
SN - 0019-3577
VL - 23
SP - 715
EP - 732
JO - Indagationes Mathematicae
JF - Indagationes Mathematicae
IS - 4
ER -