Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Let F be an infinite field of characteristic different from two and E be the infinite dimensional Grassmann algebra over F. We consider the upper triangular matrix algebra UT2(E) with entries in E endowed with the Z(2)-grading inherited by the natural Z(2)-grading of E and we study its ideal of Z(2)-graded polynomial identities (T-Z2-ideal) and its relatively free algebra. In particular we show that the set of Z(2)-graded polynomial identities of UT2(E) does not depend on the characteristic of the field. Moreover we compute the Z(2)-graded Hilbert series of UT2(E) and its Z(2)-graded Gelfand-Kirillov dimension. (C) 2015 Elsevier Inc. All rights reserved.471 469499Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)"Para mulheres na Ciencia" (L'oreal/Academia Brasileira de Ciencias/UNESCO)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)FAPESP [2013/06752-4]CNPq [305339/2013-3]