Abstract
Let [Formula: see text] be a superalgebra with superinvolution or graded involution over a field of characteristic zero and let [Formula: see text], [Formula: see text], be the [Formula: see text]-cocharacter of [Formula: see text]. The ∗-colengths sequence, [Formula: see text], [Formula: see text], is the sum of the multiplicities in the decomposition of the [Formula: see text]-cocharacter [Formula: see text], for all [Formula: see text]. The main purpose of this paper is to classify the superalgebras with superinvolution with ∗-colengths sequence bounded by three. Moreover, we shall extend to the general case, the analogous result proved by do Nascimento and Vieira in [Superalgebras with graded involution and star-graded colength bounded by 3, Linear Multilinear Algebra 67(10) (2019) 1999–2020] for finite-dimensional superalgebras with graded involution.
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