On Z2-graded identities of UT2(E) and their growth

Abstract 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 UT 2 ( 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 Z 2 -ideal) and its relatively free algebra. In particular we show that the set of Z 2 -graded polynomial identities of UT 2 ( E ) does not depend on the characteristic of the field. Moreover we compute the Z 2 -graded Hilbert series of UT 2 ( E ) and its Z 2 -graded Gelfand–Kirillov dimension.