Finite basis problem for involution monoids of unitriangular boolean matrices

Wen Ting Zhang, Yanfeng Luo, Nan Wang

Abstract:

Let (BUn,*) be the involution monoid of all Boolean upper triangular nXn matrices with 1s on the main diagonal under the ordinary matrix multiplication and the skew transposition. The involution monoid (BU2,*) is easily seen to be finitely based. In this paper, we shown that
(BUn,*) is non-finitely based for each n>=3, which answers an open question posed by Auinger et al. Therefore involution monoid (BUn,*) is finitely based if and only if n=2.